真题
名校
1 . 如图,面积为
的正方形
中有一个不规则的图形M,可按下面方法估计M的面积:在正方形
中随机投掷
个点,若
个点中有
个点落入M中,则M的面积的估计值为
. 假设正方形
的边长为2,M的面积为1,并向正方形
中随机投掷10 000个点,以
表示落入M中的点的数目.
![](https://img.xkw.com/dksih/QBM/2010/8/13/1569813231534080/1569813236465664/STEM/2871aba4-c059-466d-aefd-e8cc6d244aa9.png?resizew=176)
(Ⅰ)求
的均值
;
(Ⅱ)求用以上方法估计M的面积时,M的面积的估计值与实际值之差在区间
内的概率.
附表:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ee78b180a559ccac372776563bde4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1380ed29973304fbbcab50f6f3c7bb6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://img.xkw.com/dksih/QBM/2010/8/13/1569813231534080/1569813236465664/STEM/2871aba4-c059-466d-aefd-e8cc6d244aa9.png?resizew=176)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809bea8ceacc497b23a74f4ab3307327.png)
(Ⅱ)求用以上方法估计M的面积时,M的面积的估计值与实际值之差在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ce40cd6f61fc5a2dfd3199914c5ea0.png)
附表:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ee78b180a559ccac372776563bde4f.png)
![]() | 2424 | 2425 | 2574 | 2575 |
![]() | 0.0403 | 0.0423 | 0.9570 | 0.9590 |
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2016-11-30更新
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4卷引用:甘肃省民乐县第一中学2020-2021学年高三上学期1月诊断考试数学(理)试题