问题
解答题
为备战2012年伦敦奥运会，甲、乙两位射击选手进行了强化训练．现分别从他们的强化训练期间的若干次平均成绩中随机抽取8次，记录如下：
甲：8.3 9.0 7.9 7.8 9.4 8.9 8.4 8.3；
乙：9.2 9.5 8.0 7.5 8.2 8.1 9.0 8.5．
（Ⅰ）现要从中选派一人参加奥运会封闭集训，从统计学角度，你认为派哪位选手参加合理？简单说明理由；
（Ⅱ）若将频率视为概率，对两位选手在今后各自的二次比赛成绩进行预测，求这四次成绩中恰有两次不低于8.5分的概率．
答案
（Ⅰ）可计算出
甲=8.5，. x
乙=8.5．. x
S2甲=
[0.04+0.25+0.36+0.49+0.81+0.16+0.01+0.04]=1 8
=0.27．2.16 8
S2乙=
[0.49+1+0.25+1+0.09+0.16+0.25+0]=1 8
=0.405．3.24 8
故甲、乙两位射击选手的水平相当，但甲的发挥更稳定一些，故选择甲去．
（Ⅱ）甲的成绩不低于8.5的概率为p1=
，乙的成绩不低于8.5的概率为p2=3 8
=4 8
．1 2
于是所求概率等于C 12
•3 8
×5 8 C 12
•1 2
+(1 2
)2×(3 8
)2+(1 2
)2×(5 8
)2=1 2
=60+9+25 64×4
．47 128
所以，这四次成绩中恰有两次不低于8.5的概率为
．47 128
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