18.
某中学高三年级有学生500人,其中男生300人,女生200人.为了研究学生的数学成绩是否与性别有关,采用分层抽样的方法,从中抽取了100名学生,统计了他们期中考试的数学分数,然后按照性别分为男、女两组,再将两组的分数分成5组:
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%5B%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E100%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmn%3E110%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%5B%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E110%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmn%3E120%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%5B%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E120%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmn%3E130%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%5B%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E130%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmn%3E140%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmrow%3E%3Cmo%3E%5B%3C%2Fmo%3E%3Cmrow%3E%3Cmn%3E140%3C%2Fmn%3E%3Cmo%3E++%EF%BC%8C+%3C%2Fmo%3E%3Cmn%3E150%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmo%3E%5D%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
分别加以统计,得到如图所示的频率分布直方图.
(I)从样本分数小于110分的学生中随机抽取2人,求两人恰为一男一女的概率;
(II)若规定分数不小于130分的学生为“数学尖子生”,请你根据已知条件完成2×2列联表,并判断是否有90%的把握认为“数学尖子生与性别有关”?
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