题干

某种产品的质量以其质量指标值衡量,并依据质量指标值划分等极如下表:

质量指标值m

m<185

185≤m<205

m≥205

等级

三等品

二等品

一等品

从某企业生产的这种产品中抽取200件,检测后得到如下的频率分布直方图:

(Ⅰ)根据以上抽样调查数据,能否认为该企业生产的这种产品符合“一、二等品至少要占全部产品90%”的规定?

(Ⅱ)在样本中,按产品等极用分层抽样的方法抽取8件,再从这8件产品中随机抽取4件,求抽取的4件产品中,一、二、三等品都有的概率;

(III)该企业为提高产品质量,开展了“质量提升月”活动,活动后再抽样检测,产品质量指标值X近似满足X~N(218,140}),则“质量提升月”活动后的质量指标值的均值比活动前大约提升了多少?

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答案(点此获取答案解析)

解:(Ⅰ)根据抽样调查数据,一、二等品所占比例的估计值为0.200+0.300+0.260+0.090+0.025=0.875,

由于该估计值小于0.90,

故不能认为该企业生产的这种产品符合“一、二等品至少要占全部产品90%”的规定.

(Ⅱ)由频率分布直方图知,一、二、三等品的频率分别为0.375、0.5、0.125,

故在样本中用分层抽样方法抽取的8件产品中,一等品3件,二等品4件,三等品1件,

再从这8件产品中随机抽取4件,一、二、三等品都有的

同类题5

根据材料内容,选择正确答案。


    One day a man found a cocoon(茧) of a butterfly in the forest. He sat there for several hours and watched the butterfly. Suddenly a small opening appeared, and the butterfly made its great effort to force its body through that little hole. Then it seemed to stop making any progress. It appeared as if it had gotten as far as it could and it could go no further.

    So the man decided to help the butterfly. He cut off the remaining bit of the cocoon so that the butterfly could come out easily. But to his surprise, the butterfly got a heavy body and very small wings when it came out of the cocoon.

    The man continued to watch the butterfly because he expected that the body would grow smaller at any moment and the wings would become larger and be able to fly. But neither happened! In fact, the butterfly spent the rest of its life crawling(爬) around with a heavy body and small wings. It was never able to fly.

    The man was in his kindness, but he did not understand the nature rules. Before the butterfly came out of the cocoon, fluid(流体) from its body must be forced into its wings, and then it would be ready for flying. It must have a hard struggle(拼搏) to get through the small opening to get its freedom from the cocoon.

    Sometimes struggles are exactly what we need in our life. If God allowed us to go through our life without any difficulties, it would make us fail. We would not be as strong as we could have been, we could never fly.