1 . 已知抛一枚质地均匀的硬币100次,其中正面向上的次数
近似看成服从正态分布,则我们可以估计P(45≤
≤60)为___________ %(保留两位有效数字).(P(|
-
|≤σ)≈68.3%,P(|
-
|≤2σ)≈95.4%,P(|
-
|≤3σ)≈99.7%)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
您最近一年使用:0次
2 . 温室效应对我们的生存环境提出了挑战,节能减排是全人类的共识.某地区从当地居民的户月均用电量中随机地抽取了一批数据,将其分成
组作出了频率分布直方图,如图:
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253610491904/2716459014561792/STEM/cb15db58c71d461496ff8f60f7cc0730.png?resizew=298)
(1)试估计该地区月均用电量的平均值和标准差(同一组中的数据用该组区间的中点值作代表,精确到个位);
(2)由直方图可以认为,该地区居民的户月均用电量服从正态分布
,其中
近似为样本平均值,
近似为样本方差,这样得到正态分布的密度曲线
,如图,用随机模拟的方法向曲线
与
轴之间的区域投掷
个点,
表示落入阴影部分的点的数目.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253610491904/2716459014561792/STEM/02eb7266-5b50-4535-9200-24974bd9627a.png?resizew=289)
(i)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124c2c4e61b8e43e6b686abc7178e7ba.png)
(正态分布的近似值为
,
,
);
(ii)可以用
作为概率
的估计值,试求这种估计的误差不超过
的概率.
附表:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a306e8cf88af5a55398937adb5676a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253610491904/2716459014561792/STEM/cb15db58c71d461496ff8f60f7cc0730.png?resizew=298)
(1)试估计该地区月均用电量的平均值和标准差(同一组中的数据用该组区间的中点值作代表,精确到个位);
(2)由直方图可以认为,该地区居民的户月均用电量服从正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c980b923a1f7f2cb9ffb341ca4d68c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742d3e642d52e01899f66df411100838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b0fb37fb75f7dd0f4feae95e3c9114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b0fb37fb75f7dd0f4feae95e3c9114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadc63e6e33743ce590ed968948a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712253610491904/2716459014561792/STEM/02eb7266-5b50-4535-9200-24974bd9627a.png?resizew=289)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124c2c4e61b8e43e6b686abc7178e7ba.png)
(正态分布的近似值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c6c91509f2a6c88bc08d915fec7e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9352fdd724a2e6b5839c733b32194d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129d408d4124acf7667735bc3549d1db.png)
(ii)可以用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50759670db735a4cfdd0a7e7e5802a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fd49c18faa4d01737dc1a6cb30010a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042e234d538bc2c789d7c5a314f1ca92.png)
附表:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a306e8cf88af5a55398937adb5676a.png)
![]() | 995 | 996 | 997 | 998 |
![]() | 0.1885 | 0.3528 | 0.5771 | 0.8013 |
您最近一年使用:0次