1 . 为了解某品种一批树苗生长情况,在该批树苗中随机抽取了容量为120的样本,测量树苗高度(单位:
,经统计,其高度均在区间
,
内,将其按
,
,
,
,
,
,
,
,
,
,
,
分成6组,制成如图所示的频率分布直方图.其中高度为
及以上的树苗为优质树苗.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/69ce41f9-ffee-4d6f-8dbf-3cb41f8ab35f.png?resizew=229)
(1)求图中
的值,并估计这批树苗的平均高度(同一组中的数据用该组区间的中点值作代表);
(2)已知所抽取的这120棵树苗来自
,
两个试验区,部分数据如下列联表:
将列联表补充完整,并判断是否有
的把握认为优质树苗与
,
两个试验区有关系,并说明理由.
下面的临界值表仅供参考:
(参考公式:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e4fea666183ad7f311f188c7ebc54d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3b81b0af59d19839af077f7746ce92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e14f0292ebe0d9bbc93f0b62a66bddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3b81b0af59d19839af077f7746ce92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223637901ac3fea9a95888e98ae27e06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b1e64cbd70e8b12570ef56bc0b5a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1659c200103b9e6ade39a0d75a4662d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76feb933a6debe7e9333d5cda350537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfe4141a4636816d4e7ff2ffaec236f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91089d04e6f4af494a7f81eecda1394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ceba812c7432c5135987b6f269c066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793fa9e6d845c1fbbdddb5b9fc062b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71188e63ad147215ab513bed1ec488e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3ad3a52f6d7b683832df8e81795819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e14f0292ebe0d9bbc93f0b62a66bddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682f784fed24984dc4edc93a93548fbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/69ce41f9-ffee-4d6f-8dbf-3cb41f8ab35f.png?resizew=229)
(1)求图中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知所抽取的这120棵树苗来自
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![]() | ![]() | 合计 | |
优质树苗 | 20 | ||
非优质树苗 | 60 | ||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ca40b5a7476f844dad0e5f79fa69aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
下面的临界值表仅供参考:
![]() | 0.15 | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 |
![]() | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
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2019-04-14更新
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2卷引用:【省级联考】甘肃省2019届高三第一次高考诊断考试数学(文)试题