1 . 有一片产量很大的水果种植园,在临近成熟时随机摘下某品种水果100个,其质量(均在1至
)频数分布表如下(单位:
):
以各组数据的中间值代表这组数据的平均值,将频率视为概率.
(1)由种植经验认为,种植园内的水果质量
近似服从正态分布
,其中
近似为样本平均数
,
.请估计该种植园内水果质量在
内的百分比;
(2)现在从质量为
,
,
的三组水果中,用分层抽样方法抽取8个水果,再从这8个水果中随机抽取2个.若水果质量在
,
,
的水果每销售一个所获得的利润分别为2元,4元,6元,记随机抽取的2个水果总利润为
元,求
的分布列和数学期望.
附:若
服从正态分布
,则
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cfd3e40894c3b55b3975869c29e893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac7e61a7ea683858db47ff92d7f7074.png)
分组 | ![]() | ![]() | ![]() | ![]() | ![]() |
频数 | 10 | 30 | 40 | 15 | 5 |
(1)由种植经验认为,种植园内的水果质量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.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/e61e6f27ff8b7052f6d6414ed6fa380b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62a97edd63eb58c0449b21cdd55ed27.png)
(2)现在从质量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9fde148c96702aea4358cf7616c9b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2c568583f0d1b2855a256d15133c3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85420e98769151344c3a5b82a49ca8cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9fde148c96702aea4358cf7616c9b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2c568583f0d1b2855a256d15133c3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85420e98769151344c3a5b82a49ca8cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
附:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5580e9e19784002b11b51a68cc512e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d59748eac4045ac92b07bd0d4c10ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ae1f9c5742f1c3451b6efc9808718c.png)
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