名校
解题方法
1 . 一家养鸡场养了甲、乙两个品种的产蛋鸡,在甲、乙两个品种的产蛋鸡中各随机抽取1000只,分别记录其日产蛋量.根据产蛋期的记录,绘制了日产蛋量的频率分布直方图,如图所示(视频率为概率).
![](https://img.xkw.com/dksih/QBM/2021/10/28/2838980501135360/2842718991859712/STEM/2fef01ae-ba90-449a-bbdf-a53335f6d3e3.png?resizew=334)
![](https://img.xkw.com/dksih/QBM/2021/10/28/2838980501135360/2842718991859712/STEM/0dfa68f6-72fb-4d87-ad8c-e4ac1f61afeb.png?resizew=282)
(1)若甲、乙两种鸡的日产蛋量相互独立,记“甲、乙两种鸡的日产蛋量都不低于850个”为事件
,试估计事件
发生的概率;
(2)由于甲、乙两种鸡的食量和产蛋的大小不同,甲品种1000只鸡的日产蛋量小于850个的利润率为
,日产蛋量不小于850个而小于900个的利润为
,日产蛋量不小于900个的利润率为
;乙品种1000只鸡的日产蛋量小于850个的利润率为
,日产蛋量不小于850个而小于900个的利润为
,日产蛋量不小于900个的利润率为
.若在甲、乙两个品种上各投资10万元,
(单位:万元)和
(单位:万元)分别表示投资甲、乙两个品种所获得的利润,求
和
的数学期望,并对甲、乙两个品种的投资进行分析比较.
![](https://img.xkw.com/dksih/QBM/2021/10/28/2838980501135360/2842718991859712/STEM/2fef01ae-ba90-449a-bbdf-a53335f6d3e3.png?resizew=334)
![](https://img.xkw.com/dksih/QBM/2021/10/28/2838980501135360/2842718991859712/STEM/0dfa68f6-72fb-4d87-ad8c-e4ac1f61afeb.png?resizew=282)
(1)若甲、乙两种鸡的日产蛋量相互独立,记“甲、乙两种鸡的日产蛋量都不低于850个”为事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)由于甲、乙两种鸡的食量和产蛋的大小不同,甲品种1000只鸡的日产蛋量小于850个的利润率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de0640bc12a9b2ffd7247fa20f1dafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bbb0e8bcaf05c92ce1e616ece120b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23466fd31d0666cb9f65dced41188359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bbb0e8bcaf05c92ce1e616ece120b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23466fd31d0666cb9f65dced41188359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de0640bc12a9b2ffd7247fa20f1dafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
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2021-11-02更新
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2卷引用:广东省揭阳市揭东区第二中学2023届高三上学期第一次月考数学试题