某校100名学生某次数学考试成绩(单位:分)的频率分布直方图如下:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/110df8c5-ae51-48e3-9f88-f36e347dafce.png?resizew=267)
(1)求频率分布直方图中a的值;
(2)分别求出成绩落在
与
中的学生人数;
(3)估计78分以上的人数.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/110df8c5-ae51-48e3-9f88-f36e347dafce.png?resizew=267)
(1)求频率分布直方图中a的值;
(2)分别求出成绩落在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7bcabecab8e70c347a6b1ee691d8a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfd2d0bc6cb708c328c82daafa42c39.png)
(3)估计78分以上的人数.
更新时间:2019-09-27 16:14:08
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【推荐1】某大学为调研学生在
、
两家餐厅用餐的满意度,从在
、
两家都用过餐的学生中随机抽取了
人,每人分别对这两家餐厅进行评分,满分均为
分.整理评分数据,将分数以
为组距分为
组:
、
、
、
、
、
,得到
餐厅分数的频率分布直方图和
餐厅分数的频数分布表:
![](https://img.xkw.com/dksih/QBM/2021/4/1/2690577812996096/2690677812764672/STEM/96af20a7-410c-487d-a2d0-d053cfeda29d.png?resizew=287)
![](https://img.xkw.com/dksih/QBM/2021/4/1/2690577812996096/2690677812764672/STEM/9385110b-a3c9-4635-97c8-f499ccf22ef9.png?resizew=220)
(1)在抽样的
人中,求对
餐厅评分低于
的人数;
(2)从对
餐厅评分在
范围内的人中随机选出
人,求
人中恰有
人评分在
范围内的概率.
(3)如果从
、
两家餐厅中选择一家用餐,你会选择哪一家?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3779b4ea5477aebfe85113b0de1d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57647ca5a2273db70121674483a13fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291d2d24f859344e7635d92d0c2a142e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84df66c42058b0df3e0bceb981f962e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81c4549b234dbfa6fee74012cc7dc2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2021/4/1/2690577812996096/2690677812764672/STEM/96af20a7-410c-487d-a2d0-d053cfeda29d.png?resizew=287)
![](https://img.xkw.com/dksih/QBM/2021/4/1/2690577812996096/2690677812764672/STEM/9385110b-a3c9-4635-97c8-f499ccf22ef9.png?resizew=220)
(1)在抽样的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c7539ed297ea63b9ace6f5cc58ca8.png)
(2)从对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b446d7800e73fe9e649eaa7f89896f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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(3)如果从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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【推荐2】某班主任利用周末时间对该班级
年最后一次月考的语文作文分数进行统计,发现分数都位于
之间,现将所有分数情况分为
、
、
、
、
、
、
共七组,其频率分布直方图如图所示,已知
.
![](https://img.xkw.com/dksih/QBM/2020/8/13/2527220852441088/2530734755192832/STEM/bfa2965246b049558c9257619d71c9aa.png?resizew=407)
(1)求频率分布直方图中
、
的值;
(2)求该班级这次月考语文作文分数的平均数和中位数.(每组数据用该组区间中点值作为代表)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f95463e4696bcb6ed28581bad689d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46c004760609f420f82cf208cc423c0.png)
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(1)求频率分布直方图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求该班级这次月考语文作文分数的平均数和中位数.(每组数据用该组区间中点值作为代表)
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【推荐3】汽车的普及给人们的出行带来了诸多方便,但汽车超速行驶也造成了诸多隐患.为了解汽车通过某一段公路时的车辆行驶情况,现随机抽测了通过这段公路的200辆汽车的行驶速度(单位:km/h),所得数据均在区间
内,其频率分布直方图如图所示.
![](https://img.xkw.com/dksih/QBM/2020/2/28/2408917238759424/2408993745035264/STEM/3877245f-06a6-436f-b7b0-19f7ed7e87ef.png)
(1)求被抽测的200辆汽车的平均行驶速度.
(2)已知该路段属于事故高发路段,交警部门对此路段过往车辆限速60 km/h,并且对于超速行驶车辆有相应处罚:记分(扣除驾驶员驾照的分数)和罚款.
罚款情况如下:
求被抽测的200辆汽车中超速10%~20%的车辆数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37355114ad393d65dca03bb4567513d2.png)
![](https://img.xkw.com/dksih/QBM/2020/2/28/2408917238759424/2408993745035264/STEM/3877245f-06a6-436f-b7b0-19f7ed7e87ef.png)
(1)求被抽测的200辆汽车的平均行驶速度.
(2)已知该路段属于事故高发路段,交警部门对此路段过往车辆限速60 km/h,并且对于超速行驶车辆有相应处罚:记分(扣除驾驶员驾照的分数)和罚款.
罚款情况如下:
超速情况 | 10%以内 | 10%~20% | 20%~50% | 50%以上 |
罚款情况 | 0元 | 100元 | 150元 | 500元 |
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