(06年湖北卷文)(12分)某单位最近组织了一次健身活动,活动分

06年湖北卷文)12分)

某单位最近组织了一次健身活动,活动分为登山组和游泳组,且每个职工至多参加了其中一组。在参加活动的职工中,青年人占42.5%,中年人占47.5%,老年人占10%。登山组的职工占参加活动总人数的,且该组中,青年人占50%,中年人占40%,老年人占10%。为了了解各组不同的年龄层次的职工对本次活动的满意程度,现用分层抽样的方法从参加活动的全体职工中抽取一个容量为200的样本。试确定

(Ⅰ)游泳组中,青年人、中年人、老年人分别所占的比例;

(Ⅱ)游泳组中,青年人、中年人、老年人分别应抽取的人数。

答案

解析:(Ⅰ)设登山组人数为,游泳组中,青年人、中年人、老年人各占比例分别为abc,则有,解得b=50%,c=10%.

a=100%50%10%=40%,即游泳组中,青年人、中年人、老年人各占比例分别为40%、

50%、10%。

(Ⅱ)游泳组中,抽取的青年人数为(人);抽取的中年人数为

50%=75(人);抽取的老年人数为10%=15(人)。

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