1 . 为加强对企业产品质量的管理,市监局到区机械厂抽查机器零件的质量,共抽取了600件螺帽,将它们的直径和螺纹距之比
作为一项质量指标,由测量结果得如下频率分布直方图:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/a602cbaf-2afd-4ccb-a4dd-f4431d0acc43.png?resizew=304)
(Ⅰ)求这600件螺帽质量指标值的样本平均数
,样本方差
(在同一组数据中,用该区间的中点值作代表);
(Ⅱ)由频率分布直方图可以近似的认为,这种螺帽的质量指标值
服从正态分布
,其中
近似为样本平均数
,
近似为样本方差
.
(ⅰ)利用该正态分布,求
;
(ⅱ)现从该企业购买了100件这种螺帽,记
表示这100件螺帽中质量指标值位于区间
的件数,利用(ⅰ)的结果,求
.
附:
.若
,则
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/a602cbaf-2afd-4ccb-a4dd-f4431d0acc43.png?resizew=304)
(Ⅰ)求这600件螺帽质量指标值的样本平均数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcb21cc59fa1a45e1a0757d59dec092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e753e3587cebbc15796c35e0b34d538.png)
(Ⅱ)由频率分布直方图可以近似的认为,这种螺帽的质量指标值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8b9ad2fcfff3dd546c5fdbedfe6238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5580e9e19784002b11b51a68cc512e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcb21cc59fa1a45e1a0757d59dec092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c82e57f20f9fff9c51ae752521fb144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e753e3587cebbc15796c35e0b34d538.png)
(ⅰ)利用该正态分布,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4844f289b10f348022b838375eb1bdfb.png)
(ⅱ)现从该企业购买了100件这种螺帽,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85df8f5ad3fe9318f92b80e9a3286fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97aece7763179494a38df81089f5b8b2.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a40eb6686e14b5338914ce5dc838fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd48a80237dd53669f10ca4eda250519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee009ebf9f7afaec93371d85c38391f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bfec6991f6325269dd423cc6a0b1fd.png)
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2 . 为了解
市高三数学复习备考情况,该市教研机构组织了一次检测考试,并随机抽取了部分高三理科学生数学成绩绘制如图所示的频率分布直方图.
![](https://img.xkw.com/dksih/QBM/2018/3/28/1912011565031424/1912612809416704/STEM/0ab5069546514409babdc0a22365e12c.png?resizew=378)
(1)根据频率分布直方图,估计该市此次检测理科数学的平均成绩
;(精确到个位)
(2)研究发现,本次检测的理科数学成绩
近似服从正态分布
(
,
约为19.3).
①按以往的统计数据,理科数学成绩能达到升一本分数要求的同学约占
,据此估计本次检测成绩达到升一本的理科数学成绩大约是多少分?(精确到个位)
②已知
市理科考生约有10000名,某理科学生此次检测数学成绩为107分,则该学生全市排名大约是多少名?
(说明:
表示
的概率,
用来将非标准正态分布化为标准正态分布,即
,从而利用标准正态分布表
,求
时的概率
,这里
,相应于
的值
是指总体取值小于
的概率,即
.参考数据:
,
,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/2018/3/28/1912011565031424/1912612809416704/STEM/0ab5069546514409babdc0a22365e12c.png?resizew=378)
(1)根据频率分布直方图,估计该市此次检测理科数学的平均成绩
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dde0f01007fc21d40fab9b8c8d2521.png)
(2)研究发现,本次检测的理科数学成绩
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350bce2010f43dcba888eea277b5dbb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fa64129d33bbeab441bdf42517dbd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0ad7e7853a069537387b5192f73844.png)
①按以往的统计数据,理科数学成绩能达到升一本分数要求的同学约占
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7eb36c773bcdf53a1cc767d6b48c40e.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(说明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788422aada3ce875f2df1df0dfb46056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71451e64757302b01faaae2c6fba345e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989caa0c1e2bddae7a47a90e483bad38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f46bb6be3519a7a3833897391725eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd362c0bd72bb94f30f94d31753360f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71451e64757302b01faaae2c6fba345e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acef20d48b59ba74398ae3393ebdaff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b701cdf2644240f030b22a449c45c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd362c0bd72bb94f30f94d31753360f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2aac6e24773ce74f96bdc6b5a065128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1440aa6c1f8ef481e6fa3c05f2689459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8f22f5a5f53a900113340f6a468937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b60bd3b904130f175089b41b248d38a.png)
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2018-03-29更新
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1911次组卷
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7卷引用:第9章 统计 单元测试(A卷知识达标)-【学霸满分】2022-2023学年高二数学下学期重难点专题提优训练(苏教版2019选择性必修第二册)
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