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(Statistics) Heights of citizens in a large population have a distribution that is symmetric about the mean m.

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by Max@Math Revolution » Sat Oct 17, 2020 12:04 am

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B

C

D

E

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Difficulty—

(Statistics) Heights of citizens in a large population have a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is greater than (m − d)?

A) 66%
B) 50%
C) 67%
D) 84%
E) 34%
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Re: (Statistics) Heights of citizens in a large population have a distribution that is symmetric about the mean m.

by Max@Math Revolution » Mon Oct 19, 2020 10:28 am
Solution: We know that the distribution is symmetric about the mean. This is the concept of Normal distribution.

Thus, the percent of the distribution equidistant from the mean on either side of it is the same.

Let the percent of the distribution less than (m- d) be x%. Thus, the percent of the distribution more than (m+ d) is also x%.

Thus, we have

=> x% + 68% + x% = 100%

=> 2x = 32%, x=16%

Thus, the percent of the distribution greater than (m − d) = 100% - x% =100%-16% = 84%.

D is the correct answer.

Answer D
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