求PREP中DEVIATION和MEAN关系3题

106.
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If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than

2.5 standard deviations from the mean?

(A) 12.0

(B) 13.5

(C) 17.0

(D) 23.5

(E) 26.5

The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television.  The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours.  The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean.  Which of the following could be the number of hours that Pat watched television last week?

(A) 30

(B) 20

(C) 18

(D) 12

(E) 6

我也搞不清楚，顶。。。

(1) 2.5 deviation=2.5*3=7.5, mean=20, 设所求数为X, 则 X>20+7.5=X>27.5 or X<20-7.5=X<12.5

(2) deviation=6, between 1 and 2 deviation below mean, mean=21, 设所求数为X,

则 21-(6*2) < X < 21-(6*1) = 9 < X < 15

(3) 设mean为X, 标准差为a, 可得联立方程式(1) X-2a=58 (2) X+3a=98, 解联立得X=74, a=8

其实平均数跟标准差的概念很简单, 就是平均数加或减标准差就可以得到答案了，希望这样解释您可以了解!

以下是引用debbiewu101在2008-9-4 8:59:00的发言：
(1) X-2a=58 (2) X+3a=98

想问一下，什么时候加，什么时候减呢

X>20+7.5=X>27.5 or X<20-7.5=X<12.5

这个也不是太懂，谢谢

1、a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean

below平均数，就是它比平均数少，所以平均数-2标准差=58

同理，above是比平均数多

2、如上面connie4895 说，标准差其实是一些数相对于平均数的浮动幅度，所以在你后面的那个问题里其实指的是一个范围，2.5倍的标准差相对于平均数20的波动范围是20-2.5*3~20+2.5*3

不知道LZ理解了米？