Que: Heights of trees in a large population have a distribution that is symmetric about.............

This topic has expert replies
User avatar
Elite Legendary Member
Posts: 3950
Joined: 24 Jul 2015
Location: Las Vegas, USA
Thanked: 19 times
Followed by:36 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Que: Heights of trees 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%

User avatar
Elite Legendary Member
Posts: 3950
Joined: 24 Jul 2015
Location: Las Vegas, USA
Thanked: 19 times
Followed by:36 members
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