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工具/批量添加题库字段数据.ipynb
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"text": [
"题号: 030091 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t1.000\n",
"题号: 001611 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.950\n",
"题号: 030092 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.700\n",
"题号: 009686 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.500\n",
"题号: 030093 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.950\n",
"题号: 009690 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.900\n",
"题号: 030094 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.650\n",
"题号: 030147 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.850\t0.950\t0.900\n",
"题号: 001628 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.600\t0.550\n",
"题号: 001623 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.850\n",
"题号: 030148 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.800\t1.000\t1.000\t0.850\n",
"题号: 009137 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.800\t0.800\t1.000\t1.000\n",
"题号: 000300 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.750\n",
"题号: 000749 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.850\n",
"题号: 004283 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t1.000\n",
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"题号: 001636 , 字段: usages 中已添加数据: 20221020\t2023届高三12班\t0.000\n",
"题号: 030091 , 字段: usages 中已添加数据: 20221020\t2023届高三02班\t0.968\n",
"题号: 001611 , 字段: usages 中已添加数据: 20221020\t2023届高三02班\t0.742\n",
"题号: 030092 , 字段: usages 中已添加数据: 20221020\t2023届高三02班\t0.581\n",
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"题号: 030093 , 字段: usages 中已添加数据: 20221020\t2023届高三02班\t1.000\n",
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"题号: 030094 , 字段: usages 中已添加数据: 20221020\t2023届高三02班\t0.452\n",
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"题号: 001628 , 字段: usages 中已添加数据: 20221020\t2023届高三02班\t0.935\t0.613\n",
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"题号: 009137 , 字段: usages 中已添加数据: 20221020\t2023届高三02班\t0.903\t0.935\t0.903\t1.000\n",
"题号: 000300 , 字段: usages 中已添加数据: 20221020\t2023届高三02班\t0.774\n",
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"题号: 030093 , 字段: usages 中已添加数据: 20221020\t2023届高三05班\t1.000\n",
"题号: 009690 , 字段: usages 中已添加数据: 20221020\t2023届高三05班\t1.000\n",
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"题号: 001623 , 字段: usages 中已添加数据: 20221020\t2023届高三05班\t1.000\n",
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"题号: 009137 , 字段: usages 中已添加数据: 20221020\t2023届高三05班\t0.865\t0.973\t0.973\t0.973\n",
"题号: 000300 , 字段: usages 中已添加数据: 20221020\t2023届高三05班\t1.000\n",
"题号: 000749 , 字段: usages 中已添加数据: 20221020\t2023届高三05班\t1.000\n",
"题号: 004283 , 字段: usages 中已添加数据: 20221020\t2023届高三05班\t0.946\n",
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"题号: 030093 , 字段: usages 中已添加数据: 20221020\t2023届高三08班\t0.968\n",
"题号: 009690 , 字段: usages 中已添加数据: 20221020\t2023届高三08班\t0.839\n",
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"题号: 001628 , 字段: usages 中已添加数据: 20221020\t2023届高三08班\t0.710\t0.516\n",
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"题号: 009137 , 字段: usages 中已添加数据: 20221020\t2023届高三09班\t0.839\t0.871\t1.000\t0.935\n",
"题号: 000300 , 字段: usages 中已添加数据: 20221020\t2023届高三09班\t0.903\n",
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"题号: 030251 , 字段: objs 中已有该数据: K0907003B\n",
"题号: 030270 , 字段: objs 中已有该数据: K0907003B\n",
"题号: 030271 , 字段: objs 中已有该数据: K0907003B\n",
"题号: 030272 , 字段: objs 中已有该数据: K0907003B\n",
"题号: 030206 , 字段: objs 中已有该数据: K0907004B\n",
"题号: 030236 , 字段: objs 中已有该数据: K0907004B\n",
"题号: 030237 , 字段: objs 中已有该数据: K0907004B\n",
"题号: 030240 , 字段: objs 中已有该数据: K0907004B\n",
"题号: 030245 , 字段: objs 中已有该数据: K0907004B\n",
"题号: 030256 , 字段: objs 中已有该数据: K0907004B\n",
"题号: 030257 , 字段: objs 中已有该数据: K0907004B\n",
"题号: 030267 , 字段: objs 中已有该数据: K0907004B\n"
]
}
],
@ -191,7 +244,7 @@
],
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
"language": "python",
"name": "python3"
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@ -205,12 +258,12 @@
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},

145
工具/批量题号选题pdf生成.ipynb
View File

@ -2,40 +2,116 @@
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}
@ -50,13 +126,32 @@
"\"\"\"---设置题目列表---\"\"\"\n",
"#字典字段为文件名, 之后为内容的题号\n",
"problems_dict = {\n",
"\"K0807002B\":\"009356\",\n",
"\"K0807003B\":\"000224,000230,003734,009357,009747,009748,009749,010552,010553,010554\",\n",
"\"K0808002B\":\"000226,000611,000624,000685,000695,000704,000812,004087,004150,004324,004750,009750,010555,010559,010560\",\n",
"\"K0808003B\":\"009751,010557,010558\",\n",
"\"K0809001B\":\"009752\",\n",
"\"K0809002B\":\"009753\",\n",
"\"K0809003B\":\"009754\",\n",
"\"K0901001B\":\"030197,030198,030262\",\n",
"\"K0901002B\":\"000232,030195\",\n",
"\"K0901003B\":\"000241\",\n",
"\"K0902002B\":\"030226\",\n",
"\"K0902003B\":\"030199,030217,030223,030224,030229\",\n",
"\"K0902004B\":\"030203,030218,030228,030266\",\n",
"\"K0903001B\":\"030219,030221,030230,030231\",\n",
"\"K0903002B\":\"030220\",\n",
"\"K0903005B\":\"030170,030200,030201,030202,030204,030233,030265\",\n",
"\"K0903006B\":\"000234,000240,030196\",\n",
"\"K0904003B\":\"000235,030242\",\n",
"\"K0904004B\":\"000239\",\n",
"\"K0904005B\":\"030207,030210,030213,030238,030239\",\n",
"\"K0905001B\":\"000236\",\n",
"\"K0905002B\":\"030208\",\n",
"\"K0905003B\":\"030212\",\n",
"\"K0905004B\":\"000233\",\n",
"\"K0906004B\":\"030211,030214,030222,030234,030244,030259,030263,030264\",\n",
"\"K0906005B\":\"030246,030247,030252,030253,030254,030255,030268\",\n",
"\"K0906007B\":\"000238\",\n",
"\"K0906008B\":\"030241\",\n",
"\"K0906009B\":\"000237,030209,030248,030249,030258,030260,030269,030274\",\n",
"\"K0906010B\":\"030225,030227,030235,030250,030261\",\n",
"\"K0907001B\":\"030215\",\n",
"\"K0907003B\":\"000242,030243,030251,030270,030271,030272\",\n",
"\"K0907004B\":\"030206,030236,030237,030240,030245,030256,030257,030267\"\n",
"}\n",
"\n",
"\"\"\"---设置题目列表结束---\"\"\"\n",
@ -198,7 +293,7 @@
],
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"kernelspec": {
"display_name": "Python 3.9.7 ('base')",
"display_name": "Python 3.8.8 ('base')",
"language": "python",
"name": "python3"
},
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
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"version": "3.8.8"
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}
}
},

501
工具/文本文件/metadata.txt
View File

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20221020 2023届高三05班 1.000 1.000 1.000
30218
K0902004B
001628
20221020 2023届高三05班 1.000 1.000
30228
K0902004B
001623
20221020 2023届高三05班 1.000
30230
K0902004B
030148
20221020 2023届高三05班 1.000 1.000 1.000 1.000
30231
K0902004B
009137
20221020 2023届高三05班 0.865 0.973 0.973 0.973
30196
K0903001B
000300
20221020 2023届高三05班 1.000
30219
K0903001B
000749
20221020 2023届高三05班 1.000
30221
K0903001B
004283
20221020 2023届高三05班 0.946
30230
K0903001B
001620
20221020 2023届高三05班 1.000 1.000
30231
K0903001B
001636
20221020 2023届高三05班 1.000
30220
K0903002B
030091
20221020 2023届高三08班 0.871
30170
K0903005B
001611
20221020 2023届高三08班 0.452
30196
K0903005B
030092
20221020 2023届高三08班 0.710
30200
K0903005B
009686
20221020 2023届高三08班 0.516
30201
K0903005B
030093
20221020 2023届高三08班 0.968
30202
K0903005B
009690
20221020 2023届高三08班 0.839
30204
K0903005B
030094
20221020 2023届高三08班 0.355
30233
K0903005B
030147
20221020 2023届高三08班 0.903 0.871 0.968
30265
K0903005B
001628
20221020 2023届高三08班 0.710 0.516
30196
K0903006B
001623
20221020 2023届高三08班 0.903
30242
K0904001B
030148
20221020 2023届高三08班 0.839 1.000 1.000 0.935
30251
K0904001B
009137
20221020 2023届高三08班 0.935 0.871 1.000 1.000
30270
K0904001B
000300
20221020 2023届高三08班 0.839
30242
K0904002B
000749
20221020 2023届高三08班 0.710
30251
K0904002B
004283
20221020 2023届高三08班 0.968
30242
K0904003B
001620
20221020 2023届高三08班 0.903 0.839
30251
K0904003B
001636
20221020 2023届高三08班 0.645
30207
K0904005B
030091
20221020 2023届高三09班 0.968
30210
K0904005B
001611
20221020 2023届高三09班 0.968
30213
K0904005B
030092
20221020 2023届高三09班 0.645
30238
K0904005B
009686
20221020 2023届高三09班 0.323
30239
K0904005B
030093
20221020 2023届高三09班 0.968
30208
K0905001B
009690
20221020 2023届高三09班 0.742
30211
K0905001B
030094
20221020 2023届高三09班 0.516
30208
K0905002B
030147
20221020 2023届高三09班 0.774 0.710 0.935
30212
K0905003B
001628
20221020 2023届高三09班 0.516 0.581
30241
K0905005B
001623
20221020 2023届高三09班 0.935
30258
K0905005B
030148
20221020 2023届高三09班 0.903 0.935 1.000 0.871
30269
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009137
20221020 2023届高三09班 0.839 0.871 1.000 0.935
30259
K0906004B
000300
20221020 2023届高三09班 0.903
30257
K0906004B
000749
20221020 2023届高三09班 0.806
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K0906004B
004283
20221020 2023届高三09班 0.903
30253
K0906004B
001620
20221020 2023届高三09班 0.613 0.419
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30214
K0906004B
30222
K0906004B
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K0906004B
30241
K0906004B
30244
K0906004B
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K0906004B
30249
K0906004B
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K0906004B
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K0906004B
30255
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K0906005B
30254
K0906005B
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K0906005B
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K0906005B
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K0906005B
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K0906005B
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K0906005B
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K0906008B
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30248
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K0906010B
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K0907001B
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K0907001B
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K0907003B
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K0907003B
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K0907004B
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K0907004B
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K0907004B
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K0907004B
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20221020 2023届高三09班 0.032

96
工具/根据目标列表批量生成对应题目的字典.ipynb
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@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
@ -14,40 +14,88 @@
},
{
"cell_type": "code",
"execution_count": 4,
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# 输入目标列表\n",
"t = \"\"\"K0807001B\n",
"K0807002B\n",
"K0807003B\n",
"K0808001B\n",
"K0808002B\n",
"K0808003B\n",
"K0808004B\n",
"K0809001B\n",
"K0809002B\n",
"K0809003B\n",
"\"\"\""
"t = \"\"\"K0901001B\n",
"K0901002B\n",
"K0901003B\n",
"K0901004B\n",
"K0902001B\n",
"K0902002B\n",
"K0902003B\n",
"K0902004B\n",
"K0903001B\n",
"K0903002B\n",
"K0903003B\n",
"K0903004B\n",
"K0903005B\n",
"K0903006B\n",
"K0904001B\n",
"K0904002B\n",
"K0904003B\n",
"K0904004B\n",
"K0904005B\n",
"K0904006B\n",
"K0904007B\n",
"K0905001B\n",
"K0905002B\n",
"K0905003B\n",
"K0905004B\n",
"K0905005B\n",
"K0906001B\n",
"K0906002B\n",
"K0906003B\n",
"K0906004B\n",
"K0906005B\n",
"K0906006B\n",
"K0906007B\n",
"K0906008B\n",
"K0906009B\n",
"K0906010B\n",
"K0907001B\n",
"K0907002B\n",
"K0907003B\n",
"K0907004B\"\"\""
]
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\"K0807002B\":\"009356\",\n",
"\"K0807003B\":\"000224,000230,003734,009357,009747,009748,009749,010552,010553,010554\",\n",
"\"K0808002B\":\"000226,000611,000624,000685,000695,000704,000812,004087,004150,004324,004750,009750,010555,010559,010560\",\n",
"\"K0808003B\":\"009751,010557,010558\",\n",
"\"K0809001B\":\"009752\",\n",
"\"K0809002B\":\"009753\",\n",
"\"K0809003B\":\"009754\",\n"
"\"K0901001B\":\"030197,030198,030262\",\n",
"\"K0901002B\":\"000232,030195\",\n",
"\"K0901003B\":\"000241\",\n",
"\"K0902002B\":\"030226\",\n",
"\"K0902003B\":\"030199,030217,030223,030224,030229\",\n",
"\"K0902004B\":\"030203,030218,030228,030266\",\n",
"\"K0903001B\":\"030219,030221,030230,030231\",\n",
"\"K0903002B\":\"030220\",\n",
"\"K0903005B\":\"030170,030200,030201,030202,030204,030233,030265\",\n",
"\"K0903006B\":\"000234,000240,030196\",\n",
"\"K0904003B\":\"000235,030242\",\n",
"\"K0904004B\":\"000239\",\n",
"\"K0904005B\":\"030207,030210,030213,030238,030239\",\n",
"\"K0905001B\":\"000236\",\n",
"\"K0905002B\":\"030208\",\n",
"\"K0905003B\":\"030212\",\n",
"\"K0905004B\":\"000233\",\n",
"\"K0906004B\":\"030211,030214,030222,030234,030244,030259,030263,030264\",\n",
"\"K0906005B\":\"030246,030247,030252,030253,030254,030255,030268\",\n",
"\"K0906007B\":\"000238\",\n",
"\"K0906008B\":\"030241\",\n",
"\"K0906009B\":\"000237,030209,030248,030249,030258,030260,030269,030274\",\n",
"\"K0906010B\":\"030225,030227,030235,030250,030261\",\n",
"\"K0907001B\":\"030215\",\n",
"\"K0907003B\":\"000242,030243,030251,030270,030271,030272\",\n",
"\"K0907004B\":\"030206,030236,030237,030240,030245,030256,030257,030267\",\n"
]
}
],
@ -84,7 +132,7 @@
],
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"kernelspec": {
"display_name": "Python 3.9.7 ('base')",
"display_name": "Python 3.8.8 ('base')",
"language": "python",
"name": "python3"
},
@ -98,12 +146,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
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"version": "3.8.8"
},
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
}
}
},

3
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@ -0,0 +1,3 @@
\relax
\ttl@finishall
\gdef \@abspage@last{1}

839
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@ -293866,7 +293866,11 @@
"030170": {
"id": "030170",
"content": "2019年, 我国施行个人所得税专项附加扣除办法, 涉及子女教育、继续教育、大病医疗、住房贷款利息、住房租金、赡养老人等六项专项附加扣除, 某单位老、中、青员工分别有$72, 108, 120$人, 现采用分层抽样的方法, 从该单位上述员工中抽取$25$人调查专项附加扣除的享受情况.\\\\\n(1) 应从老、中、青员工中分别抽取多少人?\\\\\n(2) 抽取的$25$人中, 享受至少两项专项附加扣除的员工有$6$人, 分别记为$A, B, C, D, E, F$. 享受情况见下表, 其中``\\checkmark''表示享受, ``$\\times$''表示不享受, 现从这$6$人中随机抽取$2$人接受采访.\\\\\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n项目 & 员工$A$ & 员工$B$ & 员工$C$ & 员工$D$ & 员工$E$ & 员工$F$ \\\\ \\hline\n子女教育 & \\checkmark & \\checkmark & $\\times$ & \\checkmark & $\\times$ & \\checkmark \\\\ \\hline\n继续教育 & $\\times$ & $\\times$ & \\checkmark & $\\times$ & \\checkmark & \\checkmark \\\\ \\hline\n大病医疗 & $\\times$ & $\\times$ & $\\times$ & \\checkmark & $\\times$ & $\\times$ \\\\ \\hline\n住房贷款利息 & \\checkmark & \\checkmark & $\\times$ & $\\times$ & \\checkmark & \\checkmark \\\\ \\hline\n住房租金 & $\\times$ & $\\times$ & \\checkmark & $\\times$ & $\\times$ & $\\times$ \\\\ \\hline\n赡养老人 & \\checkmark & \\checkmark & $\\times$ & $\\times$ & $\\times$ & \\checkmark \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(i) 试用所给字母列举出所有可能的抽取结果;\\\\\n(ii) 设$M$为事件``抽取的$2$人享受的专项附加扣除至少有一项相同'', 求事件$M$发生的概率.",
"objs": [],
"objs": [
"K0802003B",
"K0803002B",
"K0903005B"
],
"tags": [
"第八单元"
],
@ -293887,7 +293891,9 @@
"030171": {
"id": "030171",
"content": "有红、黄、蓝三种颜色的旗帜各$3$面, 在每种颜色的$3$面旗帜上分别标上号码$1$, $2$和$3$. 现任取$3$面, 它们的颜色与号码均不相同的概率是\\blank{50}.",
"objs": [],
"objs": [
"K0803002B"
],
"tags": [
"第八单元"
],
@ -293908,7 +293914,10 @@
"030172": {
"id": "030172",
"content": "若某群体中的成员只用现金支付的概率为$0.45$. 既用现金支付也用非现金支付的概率为$0.15$, 则不用现金支付的概率为\\blank{50}.",
"objs": [],
"objs": [
"K0805002B",
"K0806004B"
],
"tags": [
"第八单元"
],
@ -293929,7 +293938,9 @@
"030173": {
"id": "030173",
"content": "连续掷两次骰子, 出现点数之和等于$4$的概率是\\blank{50}.",
"objs": [],
"objs": [
"K0803002B"
],
"tags": [
"第八单元"
],
@ -293950,7 +293961,9 @@
"030174": {
"id": "030174",
"content": "甲、乙、丙三人同在某公司上班, 若该公司规定, 每位职工可以在每周七天中任选两天休息(如选定周一、周三), 以后不再改动, 则他们选定的两个休息日相同的概率是\\blank{50}.",
"objs": [],
"objs": [
"K0803002B"
],
"tags": [
"第八单元"
],
@ -293971,7 +293984,9 @@
"030175": {
"id": "030175",
"content": "围棋盒子中有多粒黑子和白子, 已知从中任意取出$2$粒, 都是黑子的概率为$\\dfrac 17$, 都是白子的概率为$\\dfrac{12}{35}$, 则从中任意取出$2$粒, 恰好是同一色的概率是\\blank{50}.",
"objs": [],
"objs": [
"K0806004B"
],
"tags": [
"第八单元"
],
@ -293992,7 +294007,9 @@
"030176": {
"id": "030176",
"content": "任意投掷两枚骰子, 则``出现的点数之和为奇数''的概率是\\blank{50}.",
"objs": [],
"objs": [
"K0803002B"
],
"tags": [
"第八单元"
],
@ -294034,7 +294051,9 @@
"030178": {
"id": "030179",
"content": "投掷两颗做子, 得到其向上的点数分别为$m$和$n$, 则复数$(m+n\\mathrm{i})(n-m\\mathrm{i})$为实数的概率为\\bracket{20}.\n\\fourch{$\\dfrac 13$}{$\\dfrac 14$}{$\\dfrac 16$}{$\\dfrac 1{12}$}",
"objs": [],
"objs": [
"K0803002B"
],
"tags": [
"第八单元"
],
@ -294097,7 +294116,9 @@
"030181": {
"id": "030181",
"content": "设$O$为正方形$ABCD$的中心, 在$O, A, B, C, D$中任取$3$点, 则取到的$3$点共线的概率为\\blank{50}.",
"objs": [],
"objs": [
"K0803002B"
],
"tags": [
"第八单元"
],
@ -294139,7 +294160,9 @@
"030183": {
"id": "030183",
"content": "随机抽取一个年份, 对上海市该年$11$月的天气情况进行统计, 结果如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n日期 & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9$ & $10$ & $11$ & $12$ & $13$ & $14$ & $15$ \\\\ \\hline\n天气 & 雨 & 雨 & 云 & 云 & 云 & 晴 & 晴 & 晴 & 云 & 晴 & 晴 & 云 & 晴 & 晴 & 云 \\\\ \\hline\n日期 & $16$ & $17$ & $18$ & $19$ & $20$ & $21$ & $22$ & $23$ & $24$ & $25$ & $26$ & $27$ & $28$ & $29$ & $30$ \\\\ \\hline\n天气 & 雨 & 云 & 云 & 阴 & 云 & 雨 & 雨 & 阴 & 雨 & 雨 & 雨 & 雨 & 阴 & 云 & 阴 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n注: 雨表示下雨, 云表示多云.\\\\\n(1) 在$11$月份任取一天, 估计上海市在该天不下雨的概率;\\\\\n(2) 上海市某学校拟从$11$月份的一个晴天或多云的日子开始举行连续$2$天的运动会, 估计运动会期间不下雨的概率.",
"objs": [],
"objs": [
"K0803002B"
],
"tags": [
"第八单元"
],
@ -294160,7 +294183,10 @@
"030184": {
"id": "030184",
"content": "用$K$, $A_1$, $A_2$三类不同的元件连接成一个系统, 当且仅当$K$正常工作且$A_1,A_2$至少有一个正常工作时, 系统正常工作, 已知$K$, $A_1$, $A_2$正常工作的概率分别是$0.9, 0.8, 0.8$, 且是否正常工作互相独立, 则系统正常工作的概率为\\blank{50}.",
"objs": [],
"objs": [
"K0806004B",
"K0808002B"
],
"tags": [
"第八单元"
],
@ -294181,7 +294207,9 @@
"030185": {
"id": "030185",
"content": "某中学举办电脑知识竞赛, 满分为$100$分, $80$分以上(含$80$分)为优秀, 现将参赛学生的成续进行整理后分成五组: 第一组$[50, 60)$, 第二组$[60, 70)$, 第三组$[70, 80)$, 第四组$[80, 90)$, 第五组$[90, 100]$. 其中第一、三、四、五小组的频率分别为$0.30, 0.15, 0.10, 0.05$. 而第二小组的频数是$40$, 则参赛的人数为\\blank{50}.",
"objs": [],
"objs": [
"K0807001B"
],
"tags": [
"第八单元"
],
@ -294202,7 +294230,10 @@
"030186": {
"id": "030186",
"content": "两个实习生每人加工一个零件, 加工为一等品的概率分别为$\\dfrac 56$和$\\dfrac 34$, 两个零件是否加工为一等品相互独立, 则这两个零件中恰有一个一等品的概率为\\blank{50}.",
"objs": [],
"objs": [
"K0806004B",
"K0808002B"
],
"tags": [
"第八单元"
],
@ -294223,7 +294254,9 @@
"030187": {
"id": "030187",
"content": "出租车司机从饭店到火车站途中经过六个交通岗, 假设他在各交通岗遇到红灯这一事件是相互独立的, 并且概率都是$\\dfrac 13$, 则这位司机首次遇到红灯前恰好通过了三个交通岗的概率为\\blank{50}.",
"objs": [],
"objs": [
"K0808002B"
],
"tags": [
"第八单元"
],
@ -294244,7 +294277,9 @@
"030188": {
"id": "030188",
"content": "某杀毒软件的病毒查杀比赛规则为每个软件进行四轮考核, 每轮考核中能够准确对病毒进行查杀的进入下一轮考核, 否则被淘汰, 已知某个软件在四轮考核中能够准确杀毒的概率依次是$\\dfrac 56,\\dfrac 35,\\dfrac 34,\\dfrac 13$, 凡各轮考核能否通过互不影响, 则下列结论中, 正确的是\\blank{50}(写出所有正确结论的序号).\\\\\n\\textcircled{1} 该软件通过考核的概率为$\\dfrac 18$; \\textcircled{2} 该软件在第三轮考核被淘汰的概率为$\\dfrac 18$; \\textcircled{3} 该软件至少能够通过两轮考核的概率为$\\dfrac 23$; \\textcircled{4} 在此次比赛中该软件平均考核了$\\dfrac{65}{24}$轮.",
"objs": [],
"objs": [
"K0808002B"
],
"tags": [
"第八单元"
],
@ -294265,7 +294300,9 @@
"030189": {
"id": "030189",
"content": "有$6$个相同的球, 分别标有数字$1, 2, 3, 4,5,6$, 从中有放回地随机取两次, 每次取$1$个球, 甲表示事件``第一次取出的球的数字是$1$'', 乙表示事件``第二次取出的球的数字是$2$'', 丙表示事件``两次取出的球的数字之和是$8$'', 丁表示事件``两次取出的球的数字之和是$7$'', 则\\bracket{20}.\n\\fourch{甲与丙相互独立}{甲与丁相互独立}{乙与丙相互独立}{丙与丁相互独立}",
"objs": [],
"objs": [
"K0809001B"
],
"tags": [
"第八单元"
],
@ -294286,7 +294323,10 @@
"030190": {
"id": "030190",
"content": "投掷一枚均匀硬币和一枚均匀骰子各一次, 记``硬币正面向上''为事件$A$, ``骰子向上的点数是$3$''为事件$B$, 则事件$A, B$中至少有一件发生的概率是\\bracket{20}.\n\\fourch{$\\dfrac 5{12}$}{$\\dfrac 12$}{$\\dfrac 7{12}$}{$\\dfrac 34$}",
"objs": [],
"objs": [
"K0806004B",
"K0808002B"
],
"tags": [
"第八单元"
],
@ -294349,7 +294389,9 @@
"030193": {
"id": "030193",
"content": "某同学进行重复伯努利试验研究, 把一枚质地均匀的硬币连续抛掷$1000$次, 记录得$483$次正面朝上, $517$次反面朝上, 则掷一次硬币正面朝上的概率为\\blank{50}.",
"objs": [],
"objs": [
"K0807001B"
],
"tags": [
"第八单元"
],
@ -294370,7 +294412,10 @@
"030194": {
"id": "030194",
"content": "甲、乙、丙三人在同一办公室工作, 办公室只有一部电话机, 设经过该机打进的电话是打给甲、乙、丙的概率依次为$\\dfrac 16,\\dfrac 13,\\dfrac 12$. 若在一段时间内打进三个电话, 且各个电话相互独立. 求:\\\\ \n(1) 这三个电话是打给同一个人的概率;\\\\\n(2) 这三个电话中恰有两个是打给甲的概率.",
"objs": [],
"objs": [
"K0806004B",
"K0808002B"
],
"tags": [
"第八单元"
],
@ -294391,7 +294436,10 @@
"030195": {
"id": "030195",
"content": "为了解新教材使用后某高中$400$名学生应用数学意识和创新意识能力的提高情况, 学校进行一次测验, 从中抽取了$50$名学生的成绩. 这个问题中的总体、个体、样本、样本容量分别是什么?",
"objs": [],
"objs": [
"K0901001B",
"K0901002B"
],
"tags": [
"第九单元"
],
@ -294412,7 +294460,11 @@
"030196": {
"id": "030196",
"content": "下列抽样问题中用何种抽样方法比较合理? 为什么?\\\\\n(1) 某歌星在上海体育场开演唱会, 结束后主办方抽取部分现众进行效果调研;\\\\\n(2) 地铁运营商对高峰时期乘坐地铁的乘坐体验抽取乘客进行调研.",
"objs": [],
"objs": [
"K0903001B",
"K0903005B",
"K0903006B"
],
"tags": [
"第九单元"
],
@ -294433,7 +294485,9 @@
"030197": {
"id": "030197",
"content": "一模考试后, 班主任欲了解全班同学的成绩情况, 已知班级中共$38$名同学, 期中考试考了语文、数学、英语、物理、化学、历史、政治、生物、地理共$9$门学科, 在这个调查中, 总体的容量是\\blank{50}.",
"objs": [],
"objs": [
"K0901001B"
],
"tags": [
"第九单元"
],
@ -294454,7 +294508,9 @@
"030198": {
"id": "030198",
"content": "教育部调查某地区学生的午餐情况, 在该地区的$30$个学校中每校抽取了$20$名同学做问卷调查, 此次调查的样本容量为\\blank{50}.",
"objs": [],
"objs": [
"K0901001B"
],
"tags": [
"第九单元"
],
@ -294475,7 +294531,9 @@
"030199": {
"id": "030199",
"content": "在新冠肺炎疫情中, 某校出现了一例新冠确诊病例, 需通过核酸检测调查该校园疫情传播的情况, 采用的数据获取手段应当是\\blank{50}(填写``普查''或``抽样调查'')",
"objs": [],
"objs": [
"K0902003B"
],
"tags": [
"第九单元"
],
@ -294496,7 +294554,9 @@
"030200": {
"id": "030200",
"content": "某学校用分层抽样的方法从三个年级抽取若干学生, 调查学生参加社会实践活动情况, 有关数据见下表(单位: 人), 则$x$和$y$的值分别为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\n年级 & 年级人数 & 抽样人数 \\\\ \\hline\n高一 & $1080$ & $x$ \\\\ \\hline\n高二 & $1350$ & $y$ \\\\ \\hline\n高三 & $900$ & $20$ \\\\ \\hline\n\\end{tabular}\n\\end{center}",
"objs": [],
"objs": [
"K0903005B"
],
"tags": [
"第九单元"
],
@ -294517,7 +294577,9 @@
"030201": {
"id": "030201",
"content": "甲校有$3600$名学生, 乙校有$5400$名学生, 丙校有$1800$名学生, 为统计三校学生某方面的情况, 计划采用分层抽样法, 抽取一个容量为$90$人的样本, 应在这三校分别抽取学生\\bracket{20}.\n\\fourch{$30$人, $30$人, $30$人}{$30$人, $45$人, $15$人}{$20$人, $30$人, $10$人}{$30$人, $50$人, $10$人}",
"objs": [],
"objs": [
"K0903005B"
],
"tags": [
"第九单元"
],
@ -294538,7 +294600,9 @@
"030202": {
"id": "030202",
"content": "某校新生有$600$名女生和$400$名男生. 为了解这$1000$名新生的身体素质, 采用分层抽样方法抽取$100$名学生进行体质测验, 则男生甲被抽到的概率是\\bracket{20}. \n\\fourch{$0.4$}{$0.25$}{$0.1$}{$0.001$}",
"objs": [],
"objs": [
"K0903005B"
],
"tags": [
"第九单元"
],
@ -294559,7 +294623,9 @@
"030203": {
"id": "030203",
"content": "某老师上课前先通过计算机产生一个$[1,5]$中的随机正整数$a$, 再分别按学号$a,2a,3a,\\cdots$来抽取学生回答问题, 直到没有对应学号为止, 这样的抽取学生回答问题方式是否是随机抽样, 为什么?",
"objs": [],
"objs": [
"K0902004B"
],
"tags": [
"第九单元"
],
@ -294580,7 +294646,9 @@
"030204": {
"id": "030204",
"content": "为了解某工厂开展群众体育活动的情况, 拟采用分展抽样的方法从$A, B, C$三个区中抽取$7$个工厂进行调查, 已知$A, B, C$区中分别有$18, 27, 18$个工厂.\\\\\n(1) 求从$A, B, C$区中分别抽域的工厂个数;\\\\\n(2) 若从抽取的$7$个工厂中随机抽取$2$个进行调查结果的对比, 计算这$2$个工厂中至少有$1$个来自$A$区的概率.",
"objs": [],
"objs": [
"K0903005B"
],
"tags": [
"第九单元"
],
@ -294622,7 +294690,10 @@
"030206": {
"id": "030206",
"content": "在体育课体测$1000$米时, 大多学生跑得气喘吁吁且成绩不理想, 体育老师说: ``看来, 我们班的同学体能方面问题比较大, 需要加强训练.''请你从统计的角度来讨论下面的问题:\\\\\n(1) 在这个情境中, 总体和样本分别是什么?\\\\\n(2) 你同意体育老师的说法吗? 请说明理由.",
"objs": [],
"objs": [
"K0907004B",
"K0901001B"
],
"tags": [
"第九单元"
],
@ -294643,7 +294714,9 @@
"030207": {
"id": "030207",
"content": "根据如图所示的频率分布直方图, 如果样本容量为$100$, 则在区间$[6,10)$上的数据的频数为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.15,yscale =25]\n\\draw [->] (0,0) -- (30,0) node [below] {样本数据};\n\\draw [->] (0,0) -- (0,0.11) node [left] {频率/组距};\n\\draw (0,0) node [below left] {$O$};\n\\draw (2,0) -- (2,0.02) -- (6,0.02) (6,0) -- (6,0.08) -- (10,0.08) (10,0) -- (10,0.09) -- (14,0.09) -- (14,0) (14,0.03) -- (18,0.03) -- (18,0) (18,0.03) -- (22,0.03) -- (22,0);\n\\foreach \\i in {2,6,...,22} {\\draw (\\i,0) node [below] {$\\i$};};\n\\draw (0,0.02) node [left] {$0.02$} (0,0.03) node [left] {$0.03$} (0,0.08) node [left] {$x$} (0,0.09) node [left] {$0.09$};\n\\draw [dashed] (0,0.02) -- (2,0.02) (0,0.03) -- (14,0.03) (0,0.08) -- (6,0.08) (0,0.09) -- (10,0.09);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"objs": [
"K0904005B"
],
"tags": [
"第九单元"
],
@ -294664,7 +294737,10 @@
"030208": {
"id": "030208",
"content": "一个班的语文成绩的茎叶图如图所示, 则优秀率(80及以上)为\\blank{50}, 最高分是\\blank{50}, 最低分是\\blank{50}, 中位数是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{c|ccccccccc}\n$6$ & $0$ & $3$ & $4$ & $4$ & $6$ & $7$ & $8$ & $8$ & $9$ \\\\ \n$7$ & $2$ & $3$ & $5$ & $5$ & $5$ & $6$ & $7$ & $9$ & \\\\\n$8$ & $0$ & $2$ & $3$ & $3$ & $5$ & $7$ & $9$ & & \\\\ \n$9$ & $1$ & & & & & & & & \n\\end{tabular}\n\\end{center}",
"objs": [],
"objs": [
"K0905001B",
"K0905002B"
],
"tags": [
"第九单元"
],
@ -294685,7 +294761,9 @@
"030209": {
"id": "030209",
"content": "某厂研制了一种生产高精产品的设备, 为检验新设备生产产品的某项指标有无提高, 用一台旧设备和一台新设各各生产了$10$件产品, 得到各件产品该项指标数据如下: \n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n旧设备 & $9.8$ & $10.3$ & $10.0$ & $10.2$ & $9.9$ & $9.8$ & $10.0$ & $10.1$ & $10.2$ & $9.7$ \\\\ \\hline\n新设备 & $10.1$ & $10.4$ & $10.1$ & $10.0$ & $10.1$ & $10.3$ & $10.6$ & $10.5$ & $10.4$ & $10.5$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n旧设备和新设备生产产品的该项指标的样本平均数分别记为$\\overline{x}$和$\\overline{y}$, 样本方差分别记为$S_1^2$和$S_2^2$.\\\\\n(1) 求$\\overline{x}$, $\\overline{y}$, $S_1^2$, $S_2^2$;\\\\\n(2) 判断新设备生产产品的该项指标的均值较旧设备是否有显著提高(如果$\\overline{y}-\\overline{x}\\ge 2\\sqrt{\\dfrac{S_1^2+S_2^2}2}$, 则认为新设备生产产品的该项指标的均值较旧设备有显著提高, 否则不认为有显著提高).",
"objs": [],
"objs": [
"K0906009B"
],
"tags": [
"第九单元"
],
@ -294706,7 +294784,9 @@
"030210": {
"id": "030210",
"content": "一个社会调查机构就某地居民的月收人调查了$10000$人, 并根据所得数据画了样本的频率分布直方图, 则月收入不足$3500$的人占全部居民的百分比为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 1.5,yscale = 6000]\n\\draw [->] (0,0) -- (6,0) node [below] {月收入/元};\n\\draw [->] (0,0) -- (0,0.0006) node [left] {频率/组距};\n\\draw (2,0) -- (2,0.0002) -- (2.5,0.0002) (2.5,0) -- (2.5,0.0004) -- (3,0.0004) (3,0) -- (3,0.0005) -- (3.5,0.0005) (3.5,0) -- (3.5,0.0005) -- (4,0.0005) -- (4,0) (4,0.0003) -- (4.5,0.0003) -- (4.5,0) (4.5,0.0001) -- (5,0.0001) -- (5,0);\n\\foreach \\i in {2000,2500,...,5000} {\\draw ({\\i/1000},0) node [below] {$\\i$};};\n\\foreach \\i/\\j in {0.0001/4.5,0.0002/2,0.0003/4,0.0004/2.5,0.0005/3} {\\draw (0,\\i) node [left] {$\\i$}; \\draw [dashed] (0,\\i) -- (\\j,\\i);};\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"objs": [
"K0904005B"
],
"tags": [
"第九单元"
],
@ -294727,7 +294807,10 @@
"030211": {
"id": "030211",
"content": "如图所示的茎叶图记录了甲、乙两组各$5$名工人某日的产量数据(单位: 件). 若这两组数据的中位数相等, 且平均值也相等, 则$x$和$y$的值分别为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{r|c|l}\n甲组 & & 乙组 \\\\ \\hline\n$6$ & $5$ & $9$ \\\\ \n$2\\ 5$ & $6$ & $1\\ 7\\ y$ \\\\ \n$x\\ 4$ & $7$ & $8$ \n\\end{tabular}\n\\end{center}",
"objs": [],
"objs": [
"K0905001B",
"K0906004B"
],
"tags": [
"第九单元"
],
@ -294748,7 +294831,9 @@
"030212": {
"id": "030212",
"content": "下图是根据某校某次期中考试统计语文和英语学科的得分绘制的散点图, 根据散点图可知学生的语文成绩与英语成绩\\blank{50}明显关系. (填写``存在''或``不存在'')\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\draw [->] (0,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\filldraw (1.47,1.53) circle (0.01);\n\\filldraw (0.82,0.89) circle (0.01);\n\\filldraw (1.17,1.19) circle (0.01);\n\\filldraw (1.06,1.06) circle (0.01);\n\\filldraw (0.59,0.72) circle (0.01);\n\\filldraw (1.4,1.53) circle (0.01);\n\\filldraw (0.85,0.91) circle (0.01);\n\\filldraw (1.05,1.16) circle (0.01);\n\\filldraw (0.91,0.92) circle (0.01);\n\\filldraw (0.64,0.68) circle (0.01);\n\\filldraw (0.9,0.95) circle (0.01);\n\\filldraw (0.55,0.59) circle (0.01);\n\\filldraw (1.45,1.5) circle (0.01);\n\\filldraw (0.72,0.74) circle (0.01);\n\\filldraw (0.83,0.86) circle (0.01);\n\\filldraw (0.52,0.71) circle (0.01);\n\\filldraw (1.31,1.4) circle (0.01);\n\\filldraw (0.86,1.06) circle (0.01);\n\\filldraw (1.29,1.42) circle (0.01);\n\\filldraw (0.88,0.99) circle (0.01);\n\\filldraw (0.5,0.57) circle (0.01);\n\\filldraw (1.24,1.41) circle (0.01);\n\\filldraw (0.8,0.96) circle (0.01);\n\\filldraw (0.74,0.92) circle (0.01);\n\\filldraw (1.11,1.2) circle (0.01);\n\\filldraw (1.43,1.6) circle (0.01);\n\\filldraw (0.55,0.61) circle (0.01);\n\\filldraw (0.65,0.68) circle (0.01);\n\\filldraw (1.05,1.12) circle (0.01);\n\\filldraw (0.79,0.88) circle (0.01);\n\\filldraw (0.68,0.79) circle (0.01);\n\\filldraw (0.51,0.56) circle (0.01);\n\\filldraw (1.43,1.45) circle (0.01);\n\\filldraw (1.15,1.25) circle (0.01);\n\\filldraw (0.64,0.77) circle (0.01);\n\\filldraw (1.2,1.33) circle (0.01);\n\\filldraw (0.78,0.87) circle (0.01);\n\\filldraw (1.16,1.27) circle (0.01);\n\\filldraw (0.87,0.99) circle (0.01);\n\\filldraw (0.75,0.76) circle (0.01);\n\\filldraw (1.38,1.42) circle (0.01);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"objs": [
"K0905003B"
],
"tags": [
"第九单元"
],
@ -294769,7 +294854,9 @@
"030213": {
"id": "030213",
"content": "从一批零件中抽取$80$个, 测量其直径(单位: $\\text{mm}$), 将所得数据分为$9$组: $[5.31, 5.33)$, $[5.33, 5.35)$, $\\cdots$, $[5.45, 5.47)$, $[5.47, 5.49]$, 并整理得到如图的频率分布直方图, 则在被抽取的零件中, 直径落在区间$[5.43, 5.47)$内的个数为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, yscale = 0.3, xscale = 40]\n\\draw [->] (5.3,0) -- (5.53,0) node [below] {直径/$\\text{mm}$};\n\\draw [->] (5.3,0) -- (5.3,12) node [left] {频率/组距}; \n\\draw (5.3,0) node [left] {$0$};\n\\foreach \\i/\\j in {5.31/1.25,5.33/3.75,5.35/2.5,5.37/7.5,5.39/10,5.41/8.75,5.43/6.25,5.45/5,5.47/5}\n{\\draw (\\i,0) node [below] {\\small $\\i$}; \\draw (\\i,0) -- (\\i,\\j) --++ (0.02,0) --++ (0,{-\\j});};\n\\draw (5.49,0) node [below] {\\small $5.49$};\n\\foreach \\i/\\j in {5.31/1.25,5.33/3.75,5.35/2.5,5.37/7.5,5.39/10,5.41/8.75,5.43/6.25,5.45/5}\n{\\draw (5.3,\\j) node [left] {\\small $\\j$}; \\draw [dashed] (5.3,\\j) -- (\\i,\\j);};\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"objs": [
"K0904005B"
],
"tags": [
"第九单元"
],
@ -294790,7 +294877,9 @@
"030214": {
"id": "030214",
"content": "演讲比赛共有$9$位评委分别给出某选手的原始评分, 评定该选手的成绩时, 从$9$个原始评分中去掉$1$个最高分、$1$个最低分, 得到$7$个有效评分. $7$个有效评分与$9$个原始评分相比, 不变的数字特征是\\bracket{20}.\n\\fourch{中位数}{平均数}{方差}{极差}",
"objs": [],
"objs": [
"K0906004B"
],
"tags": [
"第九单元"
],
@ -294811,7 +294900,9 @@
"030215": {
"id": "030215",
"content": "已知$100$个数据的第$25$百分位数是$9.3$, 则下列说法正确的是\\bracket{20}.\n\\onech{这$100$个数据中一定有$25$个数小于或等于$9.3$}{把这$100$个数据从小到大排列后, $9.3$是第$25$个数据}{把这$100$个数据从小到大排列后, $9.3$是第$25$个数据和第$26$个数据的平均数}{把这$100$个数据从小到大排列后, $9.3$是第$25$个数据和第$24$个数据的平均数}",
"objs": [],
"objs": [
"K0907001B"
],
"tags": [
"第九单元"
],
@ -294853,7 +294944,10 @@
"030217": {
"id": "030217",
"content": "在以下调查中, 总体、个体各是什么? 哪些适合用全面调查? 哪些适合用抽样调查?\\\\\n(1) 调查一个班级学生每周的体育锻炼时间;\\\\ \n(2) 调查一个地区结核病的发病率;\\\\\n(3) 调查一批炮弹的杀伤半径;\\\\\n(4) 调查一个水库所有鱼中草鱼所占的比例.\\\\\n请你再举一些不宜用全面调查的例子, 并说明理由.",
"objs": [],
"objs": [
"K0901001B",
"K0902003B"
],
"tags": [
"第九单元"
],
@ -294874,7 +294968,9 @@
"030218": {
"id": "030218",
"content": "由均匀材质制成的一个正$20$面体(每个面都是正三角形), 将$20$个面平分成$10$组, 第$1$组标上$0$, 第$2$组标上$1$, $\\cdots$, 第$10$组标上$9$.\\\\\n(1) 投掷正$20$面体, 若把朝上一面的数字作为投掷结果, 则出现$0, 1, 2, \\cdot , 9$是等可能的吗?\\\\ \n(2) 三个正$20$面体分别涂上红、黄、蓝三种颜色, 分别代表百位、十位、个位, 同时投掷可以产生一个三位数(百位为$0$的也看作三位数), 它是$000$至$999$范围内的随机数吗?",
"objs": [],
"objs": [
"K0902004B"
],
"tags": [
"第九单元"
],
@ -294895,7 +294991,9 @@
"030219": {
"id": "030219",
"content": "实验室的笼子里共有$100$只小白鼠, 现要从中抽取$10$只作试验用. 下列两种情况是否属于简单随机抽样? 请说明理由.\\\\\n(1) 每次不经任何挑选地抓一只, 抓满$10$只为止;\\\\\n(2) 将笼中的$100$只小白鼠按$1$到$100$编号, 任意选出编号范围内的$10$个不重复数字, 把相应编号的小白鼠作为试验用的小白鼠.",
"objs": [],
"objs": [
"K0903001B"
],
"tags": [
"第九单元"
],
@ -294916,7 +295014,9 @@
"030220": {
"id": "030220",
"content": "如果计算器只能生成$[0, 1)$内的随机数, 你有办法把它转化为$[1,100)$范围内的整数随机数吗? 转化为$[1,712)$范围内的整数随机数呢?",
"objs": [],
"objs": [
"K0903002B"
],
"tags": [
"第九单元"
],
@ -294937,7 +295037,9 @@
"030221": {
"id": "030221",
"content": "在抽样调查中, 请你说说通过``随机''选择样本的优、缺点.",
"objs": [],
"objs": [
"K0903001B"
],
"tags": [
"第九单元"
],
@ -294958,7 +295060,10 @@
"030222": {
"id": "030222",
"content": "为了合理调配电力资源, 某市欲了解全市$50000$户居民的日用电量. 若通过简单随机抽样从中抽取了$300$户进行调查, 得到其日用电量的平均数为$5.5\\text{kW}\\cdot \\text{h}$, 则可以推测全市居民用户日用电量的平均数\\bracket{20}.\n\\fourch{一定为$5.5\\text{kW}\\cdot \\text{h}$}{高于$5.5\\text{kW}\\cdot \\text{h}$}{低于$5.5\\text{kW}\\cdot \\text{h}$}{约为$5.5\\text{kW}\\cdot \\text{h}$}",
"objs": [],
"objs": [
"K0906004B",
"K0901004B"
],
"tags": [
"第九单元"
],
@ -294979,7 +295084,9 @@
"030223": {
"id": "030223",
"content": "在学生身高的调查中, 小明和小华分别独立进行了简单随机抽样调查. 小明调查的样本平均数为$166.4$, 样本量为$100$; 小华调查的样本平均数为$164.7$, 样本量为$200$. 你更愿意把哪个值作为总体平均数的估计? 是不是你选的值一定比另一个更接近总体平均数? 说说你的理由.",
"objs": [],
"objs": [
"K0902003B"
],
"tags": [
"第九单元"
],
@ -295000,7 +295107,9 @@
"030224": {
"id": "030224",
"content": "找一组数据作为总体, 自行设定样本量, 进行多次简单随机抽样. 观察样本量对估计总体平均数的影响, 并试着解释其中的原因.",
"objs": [],
"objs": [
"K0902003B"
],
"tags": [
"第九单元"
],
@ -295021,7 +295130,9 @@
"030225": {
"id": "030225",
"content": "数据$x_1,x_2,\\cdots,x_m$的平均数为$\\overline{x}$, 数据$y_1, y_2, \\cdots,y_m$的平均数为$\\overline{y}$, 证明: $\\dfrac{\\sum_{i=1}^m x_i+\\sum_{i=1}^n y_i}{m+n}=\\dfrac{m}{m+n} \\overline{x}+\\dfrac{n}{m+n} \\overline{y}$.",
"objs": [],
"objs": [
"K0906010B"
],
"tags": [
"第九单元"
],
@ -295042,7 +295153,9 @@
"030226": {
"id": "030226",
"content": "有人说: ``如果抽样方法设计得好, 用样本进行视力调查与对$24300$名学生进行视力普查的结果差不多.而且对于想要掌握学生视力状况的教育部门来说, 节省了人力、物力和财力, 抽样调查更可取.''你认为这种说法有道理吗? 为什么?",
"objs": [],
"objs": [
"K0902002B"
],
"tags": [
"第九单元"
],
@ -295063,7 +295176,9 @@
"030227": {
"id": "030227",
"content": "高二年级有男生$490$人, 女生$510$人, 张华按男生、女生进行分层, 通过分层随机抽样的方法, 得到男生、女生的平均身高分别为$170.2\\text{cm}$和$160.8\\text{cm}$.\\\\ \n(1) 如果张华在各层中按比例分配样本, 总样本量为$100$, 那么在男生、女生中分别抽取了多少名? 在这种情况下, 请估计高二年级全体学生的平均身高.\\\\\n(2) 如果张华从男生、女生中抽取的样本量分别为$30$和$70$, 那么在这种情况下, 如何估计高二年级全体学生的平均身高更合理?",
"objs": [],
"objs": [
"K0906010B"
],
"tags": [
"第九单元"
],
@ -295084,7 +295199,9 @@
"030228": {
"id": "030228",
"content": "要调查全市普通高中高一年级学生中患色盲的比例, 小明根据性别对总体进行分层, 用分层随机抽样的方法进行调查. 请你查阅有关资料, 说说这样的分层是否合理. 你觉得在选择分层变量时应注意什么?",
"objs": [],
"objs": [
"K0902004B"
],
"tags": [
"第九单元"
],
@ -295105,7 +295222,9 @@
"030229": {
"id": "030229",
"content": "下列情况中哪些适合用全面调查, 哪些适合用抽样调查? 说明理由.\\\\\n(1) 了解某城市居民的食品消费结构;\\\\ \n(2) 调查一个县各村的粮食播种面积;\\\\\n(3) 了解某地区小学生中患沙眼的人数;\\\\\n(4) 了解一批玉米种子的发芽率;\\\\\n(5) 调查一条河流的水质;\\\\\n(6) 某企业想了解其产品在市场的占有率.",
"objs": [],
"objs": [
"K0902003B"
],
"tags": [
"第九单元"
],
@ -295126,7 +295245,10 @@
"030230": {
"id": "030230",
"content": "某刊物对其读者进行满意度调查, 调查表随刊物送到读者手中, 对寄回的调查表进行分析. 这是不是一项抽样调查? 样本抽取是不是属于简单随机抽样? 为什么?",
"objs": [],
"objs": [
"K0902004B",
"K0903001B"
],
"tags": [
"第九单元"
],
@ -295147,7 +295269,10 @@
"030231": {
"id": "030231",
"content": "中央电视台希望在春节联欢晚会播出后一周内获得该节目的收视率. 下面是三名同学为电视台设计的调查方案.\\\\\n同学A: 我把这张《春节联欢晚会收视率调查表》放在互联网上, 只要上网登录该网址的人就可以看到这张表, 他们填表的信息可以很快地反馈到我的电脑中.这样, 我就可以很快统计出收视率了.\\\\\n同学B: 我给我们居民小区的每一个住户发一份是否在除夕晚上看过中央电视台春节联欢晚会的调查表, 只要一两天就可以统计出收视率.\\\\\n同学C: 我在电话号码本上随机地选出一定数量的电话号码, 然后逐个给他们打电话, 问一下他们是否收看了中央电视台春节联欢晚会, 我不出家门就可以统计出中央电视台春节联欢晚会的收视率.\\\\\n请问: 上述三名同学设计的调查方案获得比较准确的收视率的可能性大吗? 为什么?",
"objs": [],
"objs": [
"K0902004B",
"K0903001B"
],
"tags": [
"第九单元"
],
@ -295189,7 +295314,9 @@
"030233": {
"id": "030233",
"content": "一支田径队有男运动员$56$人, 女运动员$42$人, 按性别进行分层, 用分层随机抽样的方法从全体运动员中抽出一个容量为$28$的样本, 如果样本按比例分配, 那么男、女运动员应各抽取多少名?",
"objs": [],
"objs": [
"K0903005B"
],
"tags": [
"第九单元"
],
@ -295210,7 +295337,9 @@
"030234": {
"id": "030234",
"content": "数据$x_1,x_2,\\cdots,x_n$的平均数为$\\overline{x}$, 数据$y_1,y_2,\\cdots,y_n$的平均数为$\\overline{y}$, $a$, $b$为常数. 如果满足$y_1=ax_1+b$, $y_2=ax_2+b$, $\\cdots$, $y_n=ax_n+b$, 证明: $\\overline{y}=a\\overline{x}+b$.",
"objs": [],
"objs": [
"K0906004B"
],
"tags": [
"第九单元"
],
@ -295231,7 +295360,9 @@
"030235": {
"id": "030235",
"content": "已知总体划分为$3$层, 通过分层随机抽样, 得到各层的样本平均数分别为$\\overline{x},\\overline{y},\\overline{z}$.\\\\\n(1) 根据以上信息可以估计总体平均数吗? 如果不能, 还需要什么条件? 写出估计式.\\\\\n(2) 如果样本量是按比例分配, 第$1, 2, 3$层的个体数分别为$L, M, N$, 样本量分别为$l, m, n$, 证明: $\\dfrac{L}{L+M+N}\\overline{x}+\\dfrac{M}{L+M+N}\\overline{y}+\\dfrac{N}{L+M+N}\\overline{z}=\\dfrac{l}{l+m+n}\\overline{x}+\\dfrac{m}{l+m+n}\\overline{y}+\\dfrac{n}{l+m+n}\\overline{z}$.",
"objs": [],
"objs": [
"K0906010B"
],
"tags": [
"第九单元"
],
@ -295252,7 +295383,9 @@
"030236": {
"id": "030236",
"content": "校学生会希望调查学生对本学期学生活动计划的意见. 你自愿担任调查员, 并打算在学校里抽取$10\\%$的同学作为样本.\\\\ \n(1) 怎样安排抽样, 可以提高样本的代表性?\\\\\n(2) 在调查抽样中你可能遇到哪些问题?\\\\\n(3) 这些问题可能会影响什么?\\\\\n(4) 你打算怎样解决这些问题?",
"objs": [],
"objs": [
"K0907004B"
],
"tags": [
"第九单元"
],
@ -295273,7 +295406,9 @@
"030237": {
"id": "030237",
"content": "一般来说, 影响农作物收成的因素有气候、土质、田间管理水平等, 如果你是一个农村调查队成员, 要在麦收季节对你所在地区的小麦进行估产调查, 你将如何设计调查方案?",
"objs": [],
"objs": [
"K0907004B"
],
"tags": [
"第九单元"
],
@ -295294,7 +295429,9 @@
"030238": {
"id": "030238",
"content": "从某小区抽取$100$户居民用户进行月用电量调查, 发现他们的用电量都在$50\\sim 350\\text{kW}\\cdot \\text{h}$之间, 进\n行适当分组后(每组为左闭右开的区间), 画出频率分布直方图如图所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.015,yscale = 400]\n\\draw [->] (0,0) -- (450,0) node [below] {月用电量/$\\text{kW}\\cdot\\text{h}$};\n\\draw [->] (0,0) -- (0,0.008) node [left] {频率/组距};\n\\draw (0,0) node [below left] {$O$};\n\\draw (50,0) -- (50,0.0024) -- (100,0.0024) (100,0) -- (100,0.0036) -- (150,0.0036) (150,0) -- (150,0.0060) -- (200,0.0060) -- (200,0) (200,0.0044) -- (250,0.0044) -- (250,0) (250,0.0024) -- (300,0.0024) -- (300,0) (300,0.0012) -- (350,0.0012) -- (350,0);\n\\foreach \\i in {0.0012,0.0024,0.0036,0.0060} {\\draw (0,\\i) node [left] {$\\i$};};\n\\draw (0,0.0044) node [left] {$x$};\n\\foreach \\i in {50,100,...,350} {\\draw (\\i,0) node [below] {$\\i$};};\n\\draw [dashed] (0,0.0012) -- (300,0.0012) (0,0.0024) -- (50,0.0024) (100,0.0024) -- (250,0.0024) (0,0.0036) -- (100,0.0036) (0,0.0044) -- (200,0.0044) (0,0.0060) -- (150,0.0060);\n\\end{tikzpicture}\n\\end{center}\n(1) 直方图中$x$的值为\\blank{50};\\\\\n(2) 在被调查的用户中, 用电量落在区间$[100, 250)$内的户数为\\blank{50}.",
"objs": [],
"objs": [
"K0904005B"
],
"tags": [
"第九单元"
],
@ -295315,7 +295452,9 @@
"030239": {
"id": "030239",
"content": "如图, 胡晓统计了他爸爸9月的手机通话明细清单, 发现他爸爸该月共通话$60$次. 胡晓按每次通话\n时间长短进行分组(每组为左闭右开的区间), 画出了频率分布直方图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.2,yscale = 40]\n\\draw [->] (0,0) -- (40,0) node [below] {通话时间/$\\text{min}$};\n\\draw [->] (0,0) -- (0,0.09) node [left] {频率/组距};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {0.01,0.02,0.03,0.04,0.05,0.06,0.07} {\\draw (0.5,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\foreach \\i in {5,10,...,30} {\\draw (\\i,0) node [below] {$\\i$};};\n\\draw (0,0.06) -- (5,0.06) node [midway,above] {$0.060$} -- (5,0);\n\\draw (5,0.046) -- (10,0.046) node [midway,above] {$0.046$} -- (10,0);\n\\draw (10,0.024) -- (15,0.024) node [midway,above] {$0.024$};\n\\draw (15,0) -- (15,0.03) -- (20,0.03) node [midway,above] {$0.030$} -- (20,0);\n\\draw (20,0.02) -- (30,0.02) node [midway,above] {$0.020$} -- (30,0) (25,0) -- (25,0.02);\n\\end{tikzpicture}\n\\end{center}\n(1) 通话时长在区间$[15, 20)$, $[20, 30)$内的次数分别为多少?\\\\\n(2) 区间$[20, 30)$上的小长方形高度低于$[15, 20)$上的小长方形的高度, 说明什么?",
"objs": [],
"objs": [
"K0904005B"
],
"tags": [
"第九单元"
],
@ -295336,7 +295475,9 @@
"030240": {
"id": "030240",
"content": "请班上每位同学估计一下自己平均每天的课外学习时间(单位: $\\text{min}$), 然后统计数据, 作出全班同学课外学习时间的频率分布直方图, 能否由这个频率分布直方图估计出你们学校全体学生课外学习时间的分布情况? 可以用它来估计你所在地区(城市、乡镇或村庄)全体学生课外学习时间的分布情况吗? 为什么?",
"objs": [],
"objs": [
"K0907004B"
],
"tags": [
"第九单元"
],
@ -295357,7 +295498,11 @@
"030241": {
"id": "030241",
"content": "已知某市2015年全年空气质量等级如下表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\n空气质量等级(空气质量指数(AQI)) & 频数 & 频率 \\\\ \\hline\n优(AQI$\\le 50$) & $83$ & $22.8\\%$ \\\\ \\hline\n良($50<$AQI$\\le 100$) & $121$ & $33.2\\%$ \\\\ \\hline\n轻度污染($100<$AQI$\\le 150$) & $68$ & $18.6\\%$ \\\\ \\hline\n中度污染($150<$AQI$\\le 200$) & $49$ & $13.4\\%$ \\\\ \\hline\n重度污染($200<$AQI$\\le 300$) & $30$ & $8.2\\%$ \\\\ \\hline\n严重污染(AQI$>300$) & $14$ & $3.8\\%$ \\\\ \\hline\n合计 & $365$ & $100\\%$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n5月 & $240$ & $80$ & $56$ & $53$ & $92$ & $126$ & $45$ & $87$ & $56$ & $60$ \\\\ \n& $191$ & $62$ & $55$ & $58$ & $56$ & $53$ & $89$ & $90$ & $125$ & $124$ \\\\ \n& $103$ & $81$ & $89$ & $44$ & $34$ & $53$ & $79$ & $81$ & $62$ & $116$ \\\\ \n& $88$ \n\\end{tabular}\n\\end{center}\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n6月 & $63$ & $92$ & $110$ & $122$ & $102$ & $116$ & $81$ & $163$ & $158$ & $76$ \\\\\n$$ & $33$ & $102$ & $65$ & $53$ & $38$ & $55$ & $52$ & $76$ & $99$ & $127$ \\\\ \n$$ & $120$ & $80$ & $108$ & $33$ & $35$ & $73$ & $82$ & $90$ & $146$ & $95$\n\\end{tabular}\n\\end{center}\n选择合适的统计图描述数据, 并回答下列问题:\\\\ \n(1) 分析该市2016年6月的空气质量情况.\\\\\n(2) 比较该市2016年5月和6月的空气质量, 哪个月的空气质量较好?\\\\\n(3) 比较该市2016年6月与该市2015年全年的空气质量, 2016年6月的空气质量是否好于去年?",
"objs": [],
"objs": [
"K0905005B",
"K0906004B",
"K0906008B"
],
"tags": [
"第九单元"
],
@ -295378,7 +295523,11 @@
"030242": {
"id": "030242",
"content": "某市2016年6月30天的空气质量指数如下:\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$35$ & $54$ & $80$ & $86$ & $72$ & $85$ & $58$ & $125$ & $111$ & $53$ \\\\ \n$10$ & $66$ & $46$ & $36$ & $18$ & $25$ & $23$ & $40$ & $60$ & $89$ \\\\ \n$88$ & $54$ & $79$ & $14$ & $16$ & $40$ & $59$ & $67$ & $111$ & $62$ \n\\end{tabular}\n\\end{center}\n你觉得这个月的空气质量如何? 请设计适当的频率分布直方图展示这组数据, 并结合空气质量分级标准分析数据.",
"objs": [],
"objs": [
"K0904001B",
"K0904002B",
"K0904003B"
],
"tags": [
"第九单元"
],
@ -295399,7 +295548,10 @@
"030243": {
"id": "030243",
"content": "在树人中学的高一年级女生中抽样, 得到27名女生的身高数据按从小到大排序后如下表: \n\\begin{center}\n\\begin{tabular}{ccccccccc}\n$148.0$ & $149.0$ & $154.0$ & $154.0$ & $155.0$ & $155.0$ & $155.5$ & $157.0$ & $157.0$ \\\\ \n$158.0$ & $158.0$ & $159.0$ & $161.0$ & $161.0$ & $162.0$ & $162.5$ & $162.5$ & $163.0$ \\\\ \n$163.0$ & $164.0$ & $164.0$ & $164.0$ & $165.0$ & $170.0$ & $171.0$ & $172.0$ & $172.0$ \n\\end{tabular}\n\\end{center}\n估计树人中学高一年级女生的第$25$, $50$, $75$百分位数.",
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"K0907003B"
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"tags": [
"第九单元"
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@ -295420,7 +295572,9 @@
"030244": {
"id": "030244",
"content": "某学校要定制高一年级的校服, 学生根据厂家提供的参考身高选择校服规格. 据统计, 高一年级女生需要不同规格校服的频数如下表所示. \n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n校服规格 & $155$ & $160$ & $165$ & $170$ & $175$ & 合计 \\\\ \\hline\n频数 & $39$ & $64$ & $167$ & $90$ & $26$ & $386$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n如果用一个量来代表该校高一年级女生所需校服的规格, 那么在中位数、平均数和众数中, 哪个量比较合适? 试讨论用下表中的数据估计全国高一年级女生校服规格的合理性.",
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"objs": [
"K0906004B"
],
"tags": [
"第九单元"
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@ -295441,7 +295595,10 @@
"030245": {
"id": "030245",
"content": "某校举行演讲比赛, $10$位评委对两位选手的评分如下: \n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n甲 & $7.5$ & $7.5$ & $7.8$ & $7.8$ & $8.0$ & $8.0$ & $8.2$ & $8.3$ & $8.4$ & $9.9$ \\\\ \n乙 & $7.5$ & $7.8$ & $7.8$ & $7.8$ & $8.0$ & $8.0$ & $8.3$ & $8.3$ & $8.5$ & $8.5$ \n\\end{tabular}\n\\end{center}\n选手的最终得分为去掉一个最低分和一个最高分之后, 剩下$8$个评分的平均数, 那么, 这两个选手的最后得分是多少? 若直接用$10$位评委评分的平均数作为选手的得分, 两位选手的排名有变化吗? 你认为哪种评分办法更好? 为什么?",
"objs": [],
"objs": [
"K0906004B",
"K0907004B"
],
"tags": [
"第九单元"
],
@ -295462,7 +295619,9 @@
"030246": {
"id": "030246",
"content": "不经过计算, 你能给下列各组数的方差排序吗?\\\\ \n\\textcircled{1} $5, 5, 5, 5, 5, 5, 5, 5, 5$;\\\\\n\\textcircled{2} $4, 4, 4, 5, 5, 5, 6, 6, 6$;\\\\\n\\textcircled{3} $3, 3, 4, 4, 5, 6, 6, 7, 7$;\\\\\n\\textcircled{4} $2, 2, 2, 2, 5, 8, 8, 8, 8$.",
"objs": [],
"objs": [
"K0906005B"
],
"tags": [
"第九单元"
],
@ -295483,7 +295642,9 @@
"030247": {
"id": "030247",
"content": "数据$x_1, x_2, \\cdots, x_n$的方差为$s_x^2$, 数据$y_1, y_2, \\cdots,y_n$的方差为$s_y^2$, $a, b$为常数. 证明:\\\\\n(1) 如果$y_1=x_1+b$, $y_2=x_2+b$, $\\cdots$, $y_n=x_n+b$, 那么$s_y^2=s_x^2$;\\\\\n(2) 如果$y_1=ax_1$, $y_2=ax_2$, $\\cdots$, $y_n=ax_n$, 那么$s_y^2=a^2s_x^2$.",
"objs": [],
"objs": [
"K0906005B"
],
"tags": [
"第九单元"
],
@ -295504,7 +295665,10 @@
"030248": {
"id": "030248",
"content": "农场种植的甲、乙两种水稻, 在面积相等的两块稻田中连续$6$年的产量如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n品种 & 第$1$年 & 第$2$年 & 第$3$年 & 第$4$年 & 第$5$年 & 第$6$年 \\\\ \\hline\n甲/$\\text{kg}$ & $900$ & $920$ & $900$ & $850$ & $910$ & $920$ \\\\ \\hline\n乙/$\\text{kg}$ & $890$ & $960$ & $950$ & $850$ & $860$ & $890$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n哪种水稻的产量比较稳定?",
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"K0906009B"
],
"tags": [
"第九单元"
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@ -295525,7 +295689,11 @@
"030249": {
"id": "030249",
"content": "一个小商店从一家有限公司购进$21$袋白糖, 每袋白糖的标准质量是$500\\text{g}$, 为了了解这些白糖的质量情况, 称出各袋白糖的质量(单位: $\\text{g}$)如下:\n\\begin{center}\n\\begin{tabular}{ccccccc}\n$486$ & $495$ & $496$ & $498$ & $499$ & $493$ & $493$ \\\\ \n$498$ & $484$ & $497$ & $504$ & $489$ & $495$ & $503$ \\\\ \n$499$ & $503$ & $509$ & $498$ & $487$ & $500$ & $508$\n\\end{tabular}\n\\end{center}\n(1) $21$袋白糖的平均质量$\\overline{x}$是多少? 标准差$s$是多少?\\\\\n(2) 质量位于$\\overline{x}-s$与$\\overline{x}+s$之间有多少袋白糖? 所占的百分比是多少?",
"objs": [],
"objs": [
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"K0906005B",
"K0906009B"
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"tags": [
"第九单元"
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@ -295546,7 +295714,9 @@
"030250": {
"id": "030250",
"content": "某学校有高中学生$500$人, 其中男生$320$人, 女生$180$人, 有人为了获得该校全体高中学生的身高信息, 采用分层抽样的方法抽取样本, 并观测样本的指标值(单位: $\\text{cm}$), 计算得男生样本的均值为$173.5$, 方差为$17$, 女生样本的均值为$163.83$, 方差为$30.03$.\\\\ \n(1) 根据以上信息, 能够计算出总样本的均值和方差吗? 为什么?\\\\ \n(2) 如果已知男、女样本量按比例分配, 你能计算出总样本的均值和方差各为多少吗?\\\\\n(3) 如果已知男、女的样本量都是$25$, 你能计算出总样本的均值和方差各为多少吗? 它们分别作为总体均值和方差的估计合适吗? 为什么?",
"objs": [],
"objs": [
"K0906010B"
],
"tags": [
"第九单元"
],
@ -295567,7 +295737,13 @@
"030251": {
"id": "030251",
"content": "棉花的纤维长度是棉花质量的重要指标. 在一批棉花中随机抽测了$60$根棉花的纤维长度(单位: $\\text{mm}$), 按从小到大排序结果如下:\n\\begin{center}\n\\begin{tabular}{ccccccccccccccc}\n$25$ & $28$ & $33$ & $50$ & $52$ & $58$ & $59$ & $60$ & $61$ & $62$ & $82$ & $86$ & $113$ & $115$ & $140$ \\\\ \n$143$ & $146$ & $170$ & $175$ & $195$ & $202$ & $206$ & $233$ & $236$ & $238$ & $255$ & $260$ & $263$ & $264$ & $265$ \\\\ \n$293$ & $293$ & $294$ & $296$ & $301$ & $302$ & $303$ & $305$ & $305$ & $306$ & $321$ & $323$ & $325$ & $326$ & $328$ \\\\ \n$340$ & $343$ & $346$ & $348$ & $350$ & $352$ & $355$ & $357$ & $357$ & $358$ & $360$ & $370$ & $380$ & $383$ & $385$ \n\\end{tabular}\n\\end{center}\n(1) 请你选择合适的组距, 作出这个样本的频率分布直方图, 分析这批棉花纤维长度分布的特征;\\\\\n(2) 请你估计这批棉花的第$5$, $95$百分位数.",
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"objs": [
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"K0904003B",
"K0907001B",
"K0907003B"
],
"tags": [
"第九单元"
],
@ -295588,7 +295764,10 @@
"030252": {
"id": "030252",
"content": "甲、乙两台机床同时生产一种零件, 在$10$天中, 两台机床每天生产的次品数分别为:\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n甲 & $0$ & $1$ & $0$ & $2$ & $2$ & $0$ & $3$ & $1$ & $2$ & $4$ \\\\\n乙 & $2$ & $3$ & $1$ & $1$ & $0$ & $2$ & $1$ & $1$ & $0$ & $1$ \n\\end{tabular}\n\\end{center}\n分别计算这两组数据的平均数和标准差, 从计算结果看, 哪台机床的性能更好?",
"objs": [],
"objs": [
"K0906004B",
"K0906005B"
],
"tags": [
"第九单元"
],
@ -295609,7 +295788,10 @@
"030253": {
"id": "030253",
"content": "在去年的足球联赛上, 一队每场比赛平均失球数是$1.5$, 全年比赛失球个数的标准差为$1.1$; 二队每场比赛平均失球数是$2.1$, 全年失球个数的标准差是$0.4$. 你认为下列说法中哪一种是正确的, 为什么?\\\\ \n\\textcircled{1} 平均说来一队比二队防守技术好; \\textcircled{2} 二队比一队技术水平更稳定; \\textcircled{3} 一队有时表现很差, 有时表现又非常好; \\textcircled{4} 二队很少不失球.",
"objs": [],
"objs": [
"K0906004B",
"K0906005B"
],
"tags": [
"第九单元"
],
@ -295630,7 +295812,10 @@
"030254": {
"id": "030254",
"content": "数据$x_1, x_2,\\cdots , x_n$的方差和标准差分别为$s_x^2$, $s_x$, 数据$y_1, y_2, \\cdots, y_n$的方差和标准差分别为$s_y^2$, $x_y$. 若$y_1=ax_1+b$, $y_2=ax_2+b$, $\\cdots$, $y_n=ax_n+b$成立, $a,b$为常数, 证明: $s_y^2=a^2s_x^2$, $s_y=|a|s_x$.",
"objs": [],
"objs": [
"K0906004B",
"K0906005B"
],
"tags": [
"第九单元"
],
@ -295651,7 +295836,9 @@
"030255": {
"id": "030255",
"content": "数据$x_1, x_2,\\cdots , x_n$的方差$s^2=0$, 证明: 所有的$x_i \\ (i=1,2,\\cdots,n)$都相同.",
"objs": [],
"objs": [
"K0906005B"
],
"tags": [
"第九单元"
],
@ -295672,7 +295859,10 @@
"030256": {
"id": "030256",
"content": "以往的招生统计数据显示, 某所大学录取的新生高考总分的中位数基本上稳定在$550$分, 你的一位高中校友在今年的高考中得了$520$分, 你是立即劝阻他报考这所大学, 还是先进一步查阅一下这所大学以往招生的其他统计信息? 解释一下你的选择.",
"objs": [],
"objs": [
"K0907004B",
"K0902002B"
],
"tags": [
"第九单元"
],
@ -295693,7 +295883,11 @@
"030257": {
"id": "030257",
"content": "甲、乙两个班级, 一次数学考试的分数排序如下:\n\\begin{center}\n\\begin{tabular}{ccccccccccc}\n甲班\t& $51$ & $54$ & $59$ & $60$ & $64$ & $68$ & $68$ & $68$ & $70$ & $71$ \\\\ \n & $72$ & $72$ & $74$ & $76$ & $77$ & $78$ & $79$ & $79$ & $80$ & $80$ \\\\ \n & $82$ & $85$ & $85$ & $86$ & $86$ & $87$ & $87$ & $87$ & $88$ & $89$ \\\\ \n & $90$ & $90$ & $91$ & $96$ & $97$ & $98$ & $98$ & $98$ & $100$ & $100$ \\\\ \n乙班\t& $61$ & $63$ & $63$ & $66$ & $70$ & $71$ & $71$ & $73$ & $75$ & $75$ \\\\ \n & $76$ & $79$ & $79$ & $80$ & $80$ & $80$ & $81$ & $81$ & $82$ & $82$ \\\\ \n & $83$ & $83$ & $83$ & $84$ & $84$ & $84$ & $85$ & $85$ & $85$ & $85$ \\\\ \n & $85$ & $85$ & $86$ & $87$ & $87$ & $88$ & $90$ & $91$ & $94$ & $98$ \n\\end{tabular}\n\\end{center}\n请你就这次考试成绩, 对两个班级的数学学习情况进行评价.",
"objs": [],
"objs": [
"K0906004B",
"K0906005B",
"K0907004B"
],
"tags": [
"第九单元"
],
@ -295714,7 +295908,10 @@
"030258": {
"id": "030258",
"content": "有一种鱼的身体吸收汞, 一定量身体中汞的含量超过其体重的$1.00 \\text{ppm}$(即百万分之一)的鱼被人食用后, 就会对人体产生危害. 在$30$条鱼的样本中发现的汞含量(单位: $\\text{ppm}$)如下: \n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$0.07$ & $0.24$ & $0.95$ & $0.98$ & $1.02$ & $0.98$ & $1.37$ & $1.40$ & $0.39$ & $1.02$ \\\\ \n$1.44$ & $1.58$ & $0.54$ & $1.08$ & $0.61$ & $0.72$ & $1.20$ & $1.14$ & $1.62$ & $1.68$ \\\\ \n$1.85$ & $1.20$ & $0.81$ & $0.82$ & $0.84$ & $1.29$ & $1.26$ & $2.10$ & $0.91$ & $1.31$ \n\\end{tabular}\n\\end{center}\n(1) 请用合适的统计图描述上述数据, 并分析这$30$条鱼的汞含量的分布特点;\\\\ \n(2) 求出上述样本数据的平均数和标准差;\\\\\n(3) 从实际情况看, 许多鱼的汞含量超标的原因是这些鱼在出售之前没有被检测过. 你认为每批这种鱼的平均汞含量都比$1.00 \\text{ppm}$大吗?\\\\\n(4) 在上述样本中, 有多少条鱼的汞含量在以平均数为中心、$2$倍标准差的范围内?",
"objs": [],
"objs": [
"K0905005B",
"K0906009B"
],
"tags": [
"第九单元"
],
@ -295735,7 +295932,9 @@
"030259": {
"id": "030259",
"content": "在一次人才招聘会上, 有一家公司的招聘员告诉你, ``我们公司的收入水平很高''``去年, 在$50$名员工中, 最高年收入达到了$200$万, 员工年收入的平均数是$10$万'', 而你的预期是获得$9$万元年薪.\\\\\n(1) 你是否能够判断年薪为9万元的员工在这家公司算高收入者?\\\\ \n(2) 如果招聘员继续告诉你, ``员工年收入的变化范围是从$3$万到$200$万'', 这个信息是否足以使你作出自己是否受聘的决定? 为什么?\\\\\n(3) 如果招聘员继续给你提供了如下信息, 员工收入的第一四分位数为$4.5$万, 第三四分位数为$9.5$万, 你又该如何使用这条信息来作出是否受聘的决定?\\\\\n(4) 根据(3)中招聘员提供的信息, 你能估计出这家公司员工收入的中位数是多少吗? 为什么平均数比估计出的中位数高很多?",
"objs": [],
"objs": [
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"tags": [
"第九单元"
],
@ -295756,7 +295955,9 @@
"030260": {
"id": "030260",
"content": "有$20$种不同的零食, 每$100\\text{g}$可食部分包含的能量(单位: $\\text{kJ}$)如下:\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$110$ & $120$ & $123$ & $165$ & $432$ & $190$ & $174$ & $235$ & $428$ & $318$ \\\\ \n$249$ & $280$ & $162$ & $146$ & $210$ & $120$ & $123$ & $120$ & $150$ & $140$ \n\\end{tabular}\n\\end{center}\n(1) 以上述$20$个数据组成总体, 求总体平均数与总体标准差.\\\\\n(2) 设计恰当的随机抽样方法, 从总体中抽取一个容量为$7$的样本, 求样本的平均数与标\n准差.\\\\\n(3) 利用上面的抽样方法, 再抽取容量为$7$的样本, 计算样本的平均数和标准差. 这个样本的平均数和标准差与(2)中的结果一样吗? 为什么?\\\\\n(4) 利用(2)中的随机抽样方法, 分别从总体中抽取一个容量为$10, 13, 16, 19$的样本, 求样本的平均数与标准差. 分析样本容量与样本的平均数和标准差对总体的估计效果之间有什么关系.",
"objs": [],
"objs": [
"K0906009B"
],
"tags": [
"第九单元"
],
@ -295777,7 +295978,9 @@
"030261": {
"id": "030261",
"content": "已知总体划分为$3$层, 通过分层随机抽样, 各层抽取的样本量、样本平均数和样本方差分别为: $l,\\overline{x},s_1^2;m,\\overline{y},s_2^2;n,\\overline{z},s_3^2$. 记总的样本平均数为$\\overline{w}$, 样本方差为$s^2$, 证明:\\\\\n(1) $\\overline{w}=\\dfrac{l}{l+m+n}\\overline{x}+\\dfrac{m}{l+m+n}\\overline{y}+\\dfrac{n}{l+m+n}\\overline{z}$;\\\\\n(2) $s^2=\\dfrac{1}{l+m+n}(l(s_1^2+(\\overline{x}-\\overline{w})^2)+m(s_2^2+(\\overline{y}-\\overline{w})^2)+n(s_3^2+(\\overline{z}-\\overline{w})^2))$.",
"objs": [],
"objs": [
"K0906010B"
],
"tags": [
"第九单元"
],
@ -295798,7 +296001,9 @@
"030262": {
"id": "030262",
"content": "为了了解某地参加计算机水平测试的$5000$名学生的成绩, 从中抽取了$200$名学生进行调查分析, 在这个问题中, 被抽取的$200$名学生是\\bracket{20}.\n\\fourch{总体}{个体}{样本}{样本量}",
"objs": [],
"objs": [
"K0901001B"
],
"tags": [
"第九单元"
],
@ -295819,7 +296024,10 @@
"030263": {
"id": "030263",
"content": "四名同学各掷骰子$5$次, 分别记录每次骰子出现的点数, 根据四名同学的统计结果, 可以判断出一定没有出现点数$6$的是\\bracket{20}.\n\\twoch{平均数为$3$, 中位数为$2$}{中位数为$3$, 众数为$2$}{平均数为$2$, 方差为$2.4$}{中位数为$3$, 方差为$2.8$}",
"objs": [],
"objs": [
"K0906004B",
"K0906005B"
],
"tags": [
"第九单元"
],
@ -295840,7 +296048,9 @@
"030264": {
"id": "030264",
"content": "如果一组数据的中位数比平均数小很多, 下面哪种叙述一定是错误的? 为什么?\\\\ \\textcircled{1} 数据中可能有异常值; \n\\textcircled{2} 这组数据是近似对称的;\n\\textcircled{3} 数据中可能有极端大的值; \n\\textcircled{4} 数据中众数可能和中位数相同.",
"objs": [],
"objs": [
"K0906004B"
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"tags": [
"第九单元"
],
@ -295861,7 +296071,9 @@
"030265": {
"id": "030265",
"content": "(1) 在已分组的若干数据中, 每组的频数是指\\blank{50}, 每组的频率是指\\blank{50}.\n(2) 一个公司共有$N$名员工, 下设一些部门, 要采用等比例分层随机抽样的方法从全体员工中抽取样本量为$n$的样本, 如果某部门有$m$名员工, 那么从该部门抽取的员工人数是\\blank{50}.",
"objs": [],
"objs": [
"K0903005B"
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"tags": [
"第九单元"
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@ -295882,7 +296094,9 @@
"030266": {
"id": "030266",
"content": "一家著名的全国性连锁服装店进行了一项关于当年秋季服装流行色的民意调查, 调查者通过向顾客发放饮料, 并让顾客通过挑选饮料杯上印着的颜色来对自己喜欢的服装颜色``投票'', 根据这次调查结果, 在某大城市$A$, 服装颜色的众数是红色, 而当年全国服装协会发布的调查结果是咖啡色.\\\\\n(1) 这个结果是否代表$A$城市的人的看法?\\\\\n(2) 你认为这两种调查的差异是由什么引起的?",
"objs": [],
"objs": [
"K0902004B"
],
"tags": [
"第九单元"
],
@ -295903,7 +296117,9 @@
"030267": {
"id": "030267",
"content": "从一本英语书中随机抽取$100$个句子, 数出每个句子中的单词数, 作出这$100$个数据的频率分布表, 由此你可以作出什么估计?",
"objs": [],
"objs": [
"K0907004B"
],
"tags": [
"第九单元"
],
@ -295924,7 +296140,9 @@
"030268": {
"id": "030268",
"content": "在一个文艺比赛中, $12$名专业人士和$12$名观众代表各组成一个评委小组, 给参赛选手打分. 下面是两组评委对同一名选手的打分:\n\\begin{center}\n\\begin{tabular}{ccccccccccccc}\n小组A & $42$ & $45$ & $48$ & $46$ & $52$ & $47$ & $49$ & $55$ & $42$ & $51$ & $47$ & $45$ \\\\ \n小组B & $55$ & $36$ & $70$ & $66$ & $75$ & $49$ & $46$ & $68$ & $42$ & $62$ & $58$ & $47$\n\\end{tabular}\n\\end{center}\n(1) 选择一个可以度量每一组评委打分相似性的量, 并对每组评委的打分计算度量值.\\\\ \n(2) 你能据此判断小组A与小组B中哪一个更像是由专业人士组成的吗?",
"objs": [],
"objs": [
"K0906005B"
],
"tags": [
"第九单元"
],
@ -295945,7 +296163,10 @@
"030269": {
"id": "030269",
"content": "一名学生通过计步仪器, 记录了自己$100$天每天走的步数, 数据如下: \n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$5678$ & $13039$ & $8666$ & $9521$ & $8722$ & $10575$ & $2107$ & $4165$ & $17073$ & $11205$ \\\\ \n$5467$ & $11736$ & $9986$ & $8592$ & $6542$ & $12386$ & $13115$ & $5705$ & $8358$ & $13234$ \\\\ \n$20142$ & $9769$ & $10426$ & $12802$ & $16722$ & $8587$ & $9266$ & $8635$ & $2455$ & $4524$ \\\\ \n$8260$ & $13165$ & $9812$ & $9533$ & $2377$ & $5132$ & $8212$ & $7968$ & $9859$ & $3961$ \\\\ \n$5484$ & $11344$ & $8722$ & $12944$ & $8597$ & $12594$ & $15101$ & $4751$ & $11130$ & $11286$ \\\\ \n$8897$ & $7192$ & $7313$ & $8790$ & $7699$ & $10892$ & $9583$ & $9207$ & $16358$ & $10182$ \\\\ \n$3607$ & $1789$ & $9417$ & $4566$ & $12347$ & $3228$ & $7606$ & $8689$ & $8755$ & $15609$ \\\\ \n$8767$ & $9226$ & $5622$ & $11094$ & $8865$ & $11246$ & $17417$ & $7995$ & $7317$ & $6878$ \\\\ \n$4270$ & $11051$ & $5705$ & $5442$ & $10078$ & $9107$ & $8354$ & $6483$ & $16808$ & $1509$ \\\\ \n$1301$ & $10843$ & $13864$ & $12691$ & $8419$ & $14267$ & $9809$ & $9858$ & $8922$ & $12682$ \n\\end{tabular}\n\\end{center}\n(1) 画出这组数据的频率分布直方图, 并分析数据的分布特点;\\\\\n(2) 计算这组数据的平均数、中位数和标准差, 并根据这些数值描述这名学生的运动情况.",
"objs": [],
"objs": [
"K0905005B",
"K0906009B"
],
"tags": [
"第九单元"
],
@ -295966,7 +296187,12 @@
"030270": {
"id": "030270",
"content": "一家水果店的店长为了解本店苹果的日销售情况, 记录了过去$30$天苹果的日销售量(单位: $\\text{kg}$), 结果如下: \n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$83$ & $96$ & $107$ & $91$ & $70$ & $75$ & $94$ & $80$ & $80$ & $100$ \\\\ \n$75$ & $99$ & $117$ & $89$ & $74$ & $94$ & $84$ & $85$ & $101$ & $87$ \\\\ \n$93$ & $85$ & $107$ & $99$ & $55$ & $97$ & $86$ & $84$ & $85$ & $104$ \n\\end{tabular}\n\\end{center}\n(1) 请计算该水果店过去$30$天苹果日销售量的中位数、平均数、极差和标准差.\\\\\n(2) 一次进货太多, 水果会变得不新鲜; 进货太少, 又不能满足顾客的需求. 店长希望每天的苹果尽量新鲜, 又能$80\\%$地满足顾客的需求(在$100$天中, 大约有$80$天可以满足顾客的需求). 请问, 每天应该进多少千克苹果?",
"objs": [],
"objs": [
"K0904001B",
"K0906009B",
"K0907001B",
"K0907003B"
],
"tags": [
"第九单元"
],
@ -295987,7 +296213,10 @@
"030271": {
"id": "030271",
"content": "一家保险公司决定对推销员实行目标管理, 即给推销员确定一个具体的销售目标. 确定的销售目标是否合适, 直接影响到公司的经济效益. 如果目标定得过高, 多数推销员完不成任务, 会使推销员失去信心; 如果目标定得太低, 将不利于挖掘推销员的工作潜力.下面一组数据是部分推销员的月销售额(单位: 千元):\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n$19.58$ & $16.11$ & $16.45$ & $20.45$ & $20.24$ & $21.66$ & $22.45$ & $18.22$ & $12.34$ & $19.35$ \\\\ \n$20.55$ & $17.45$ & $18.78$ & $17.96$ & $19.91$ & $18.12$ & $14.65$ & $14.78$ & $16.78$ & $18.78$ \\\\ \n$18.29$ & $18.51$ & $17.86$ & $19.58$ & $19.21$ & $18.55$ & $16.34$ & $15.54$ & $17.55$ & $14.89$ \\\\ \n$18.94$ & $17.43$ & $17.14$ & $18.02$ & $19.98$ & $17.88$ & $17.32$ & $19.35$ & $15.45$ & $19.58$ \\\\ \n$13.45$ & $21.34$ & $14.00$ & $18.42$ & $23.00$ & $17.52$ & $18.51$ & $17.16$ & $24.56$ & $25.14$ \n\\end{tabular}\n\\end{center}\n请根据这组样本数据提出使$65\\%$的职工能够完成销售指标的建议.",
"objs": [],
"objs": [
"K0907001B",
"K0907003B"
],
"tags": [
"第九单元"
],
@ -296008,7 +296237,10 @@
"030272": {
"id": "030272",
"content": "为了解某市家庭用电量的情况, 该市统计局调查了$200$户居民去年一年的月均用电量(单位: $\\text{kW}\\cdot\\text{h}$), 数据从小到大排序如下:\n\\begin{center}\n\\begin{tabular}{ccccccccccccccc}\n$8$ & $18$ & $22$ & $31$ & $42$ & $48$ & $49$ & $50$ & $51$ & $56$ & $57$ & $57$ & $60$ & $61$ & $61$ \\\\ \n$61$ & $62$ & $62$ & $63$ & $63$ & $65$ & $66$ & $67$ & $69$ & $70$ & $70$ & $71$ & $72$ & $72$ & $74$ \\\\ \n$76$ & $77$ & $77$ & $78$ & $78$ & $80$ & $80$ & $82$ & $82$ & $82$ & $83$ & $84$ & $84$ & $88$ & $88$ \\\\ \n$89$ & $90$ & $91$ & $93$ & $93$ & $94$ & $95$ & $96$ & $96$ & $96$ & $97$ & $98$ & $98$ & $98$ & $99$ \\\\ \n$100$ & $100$ & $100$ & $101$ & $101$ & $101$ & $105$ & $106$ & $106$ & $106$ & $107$ & $107$ & $107$ & $107$ & $108$ \\\\ \n$108$ & $109$ & $109$ & $110$ & $110$ & $110$ & $111$ & $112$ & $113$ & $113$ & $114$ & $115$ & $116$ & $118$ & $120$ \\\\ \n$120$ & $120$ & $121$ & $123$ & $124$ & $127$ & $127$ & $127$ & $130$ & $130$ & $130$ & $131$ & $131$ & $132$ & $132$ \\\\ \n$132$ & $133$ & $133$ & $134$ & $134$ & $134$ & $135$ & $135$ & $135$ & $135$ & $136$ & $137$ & $137$ & $138$ & $139$ \\\\ \n$139$ & $140$ & $141$ & $142$ & $144$ & $146$ & $146$ & $147$ & $148$ & $149$ & $151$ & $152$ & $154$ & $156$ & $159$ \\\\ \n$160$ & $162$ & $163$ & $163$ & $164$ & $165$ & $167$ & $169$ & $170$ & $170$ & $172$ & $174$ & $174$ & $177$ & $178$ \\\\ \n$178$ & $180$ & $182$ & $182$ & $187$ & $189$ & $191$ & $191$ & $192$ & $194$ & $194$ & $200$ & $201$ & $201$ & $202$ \\\\ \n$203$ & $203$ & $206$ & $208$ & $212$ & $213$ & $214$ & $216$ & $223$ & $224$ & $237$ & $247$ & $250$ & $250$ & $251$ \\\\ \n$253$ & $254$ & $258$ & $260$ & $265$ & $274$ & $274$ & $283$ & $288$ & $289$ & $304$ & $319$ & $320$ & $324$ & $339$ \\\\\n$462$ & $498$ & $530$ & $542$ & $626$\n\\end{tabular}\n\\end{center}\n为了既满足居民的基本用电需求, 又提高能源的利用效率, 市政府计划采用阶梯电价, 使$75\\%$的居民缴费在第一档, $20\\%$的居民缴费在第二档, 其余$5\\%$的居民缴费在第三档. 请确定各档的范围.",
"objs": [],
"objs": [
"K0907001B",
"K0907003B"
],
"tags": [
"第九单元"
],
@ -296053,7 +296285,9 @@
"030274": {
"id": "030274",
"content": "针对``区域内中小学生家长对学校教育的满意程度'', 市教委于前日进行了专项调查. 反馈的打分情况如下(分数越大表示满意程度越高):\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n分数 & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ \\\\ \\hline\n频数 & $15$ & $34$ & $129$ & $478$ & $1031$ & $623$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n则该调查所反馈的分数的均值为\\blank{50}, 标准差为\\blank{50}(均精确到$0.01$).",
"objs": [],
"objs": [
"K0906009B"
],
"tags": [
"第九单元"
],