Question

．（本小题满分12分）

为了解某校高三学生质检数学成绩分布，从该校参加质检的学生数学成绩中抽取一个样本，并分成5组，绘成如图所示的频率分布直方图．若第一组至第五组数据的频率之比为，最后一组数据的频数是6．

         （Ⅰ）估计该校高三学生质检数学成绩在125～140分之间的概率，并求出样本容量；

         （Ⅱ）从样本中成绩在65～95分之间的学生中任选两人，求至少有一人成绩在65～80分之间的概率．

Answer

（Ⅰ）．（Ⅱ）．

【解析】(I)根据频数与样本容量的比就等于频率来求解即可.

(2)先分别计算出65～80分之间和成绩在80～95分之间的学生数，然后再根据古典概型概率计算公式计算即可.

（Ⅰ）估计该校高三学生质检数学成绩在125～140分之间的概率为

， ···················································································· 2分

又设样本容量为，则，解得，．············································· 4分

（Ⅱ）样本中成绩在65～80分之间的学生有=2人，记为；成绩在80～95分之间的学生=4人，记为，············································································································ 5分

从上述6人中任选2人的所有可能情形有：

 ，共15种，·························································································································· 8分

至少有1人在65～80分之间的可能情形有

共9种，········· 11分

因此，所求的概率．      12分