解题方法
1 . 某厂为检验车间一生产线是否工作正常,现从生产线中随机抽取一批零件样本,测量尺寸(单位:
)绘成频率分布直方图如图所示:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/13/8043698e-d83a-4231-818d-dc7e2474cf21.png?resizew=284)
(1)求该批零件样本尺寸的平均数
和样本方差
(同一组中的数据用该组区间的中点值作代表);
(2)若该批零件尺寸
服从正态分布
,其中
近似为样本平均数
,
近似为样本方差
,利用该正态分布求
;
(3)若从生产线中任取一零件,测量尺寸为
,根据
原则判断该生产线是否正常?
附:
;若
,则
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/13/8043698e-d83a-4231-818d-dc7e2474cf21.png?resizew=284)
(1)求该批零件样本尺寸的平均数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
(2)若该批零件尺寸
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84c2c26cbb6b22a415fd0830401aeac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742d3e642d52e01899f66df411100838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca44f0e36fc0106da97a1aa855d501d.png)
(3)若从生产线中任取一零件,测量尺寸为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56817c785e9fa0c8616ec0a58358d634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45d81fb351bc6c693fb0a114152b2d0.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79648bbbf220c4897f5c8e95d204273c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4a31b978abc6f5a426550145885adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045bc0a5899e148fa40d32e6930b2a64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7cdad6f8409491ea3b7094a692fa13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce5838c0e1659d6bf0f491ee193221a.png)
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2018-01-27更新
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2卷引用:河北省沧州市普通高中高三上学期教学质量监测(联考)数学(理)试题