关于标准差与正态分布的PS请教！

Fernee · 发表于 2018-6-23 17:00:21

题目：
For a certain examination, the scores in a large population has a distribution that is symmetric about the mean m. The scores had a mean of 60 and a standard deviation of 6. If 68% distribution lies within one standard deviation d of the mean, and 95% distribution lies within 2 standard deviations of the mean, what percentage of the distribution is between 66 and 72?
A. 2.5%
B. 13.5%
C. 27%
D. 34%
E. 47.5%
答案写的是A，不解，求指教

为什么不能面积相减除2来做？数学渣渣在这里求指教了

sanchol1994 · 发表于 2018-6-23 17:30:45

答案不是B吗？（95%-68%）/2

chad123 · 发表于 2018-6-27 13:36:33

答案错了吧，我也觉得是b.

木木质 · 发表于 2018-8-1 20:34:17

B吧，不是A

coolwawayy · 发表于 2018-10-25 17:52:51

答案是B吧~

kluivert · 发表于 2018-10-25 18:03:36

请解释下啊，俺完全不懂
谢谢

kluivert · 发表于 2018-10-25 18:08:53

献给那些和我一样不懂的人

Let's first sketch a distribution that is symmetric about the mean m.
Image
Notice that m+d represents 1 unit of standard deviation ABOVE the mean
Likewise, m-d represents 1 unit of standard deviation BELOW the mean
And m+2d represents 2 units of standard deviation ABOVE the mean, etc.
ASIDE: There are infinitely many distributions that are symmetric about the mean m. The above distribution is just one.

Our goal is to determine what portion of the population is LESS THAN than m+d
Image

First recognize that, since the distribution is symmetric about the mean m, 50% of the population is BELOW the mean, and 50% is ABOVE the mean.
Image

Next, we're told that 68% of the distribution lies within one standard deviation d of the mean
In other words, 68% the population is BETWEEN m-d and m+d
Image

Since the distribution is symmetric about the mean m, this 68%, is divided into two equal populations.
Image

When we COMBINE our two findings, we see that the percentage of the population that's below m+d = 50% + 34% = 84%
Image

Answer: D

oatmilk · 发表于 2018-10-25 18:17:56

答案绝对是B。自己画一条直线，中间一点是60，往右走1d，2d，往左走-1d，-2d，区间都是对称分布的，哪个区间的比例都能算出来

关于标准差与正态分布的PS请教！

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