问题 问答题

某地抽样调查结果表明,考生的外语成绩(百分制)近似正态分布,平均成绩为72分,96分以上的占考生总数的2.3%,试求考生的外语成绩在60分到84分之间的概率.

x 0 0.5 1.0 1.5 2.0 2.5 3.0
ψ(x) 0.500 0.692 0.941 0.933 0.977 0.994 0.999
其中φ(x)表示标准正态分布函数.

答案

参考答案:设X为考生的外语成绩,由题设知X~N(72,σ2),且P{X≥96}=2.3%=0.023,即
[*]
于是得[*]
由φ(x)的数值表知[*]
这样X~N(72,122),所求概率为
[*]

解析:[评注] 本题主要考查正态分布的应用及性质.
[考点提示] 正态分布N(μ,σ2)由数学期望μ和方差σ2唯一决定,而μ=72,因此要计算P(60≤X≤84),只要由P{X≥96

单项选择题

I first went to hear a live rock concert when I was eight years old. My brother and his friends were all fans of a heavy metal group called Black Wednesday. When they discovered that Black Wednesday were going to perform at our local theatre, they all bought (21) for the performance. However, at the last minute, once of the friends couldn’t go, so my brother offered me the ticket. I was really excited!

I remember the buzz (嘈杂声) of excitement inside the theatre as we all found our seats. After a few minutes, the lights went down and everybody became quiet. I could barely make out the stage in the (22) . We waited. Then there was a roar from the crowd, like an explosion, as the first members of the band stepped onto the stage. My brother leaned over and shouted something in my ear, but I couldn’t hear what he was saying. The first song was already starting and the music was as (23) as a jet engine. I could (24) the drum beats and bass notes in my stomach.

I can’t recall any of the songs that the band played. I just (25) that I really enjoyed the show and didn’t want it to (26) . But in the end, after three encores (加演), the show finished. We left the (27) and walked unsteadily out onto the pavement. I felt a little dizzy, as if I had just woken from a long sleep. My ears were still (28) with the beat of the last song.

After the (29) , I became a Black Wednesday fan too for a few years before getting into other kinds of music. Once in a while, though, I listen to one of their songs and (30) I’m back at that first show.

30().

A. decide

B. regret

C. conclude

D. imagine

多项选择题