A normal distribution has a mean of 55, and about 25% of the values are above 65. Approximately what is the standard deviation for this distribution?
A) 15
B) 18
C) 13
D) 20
E) 10

Question

Quizplus · Accepted Answer

The standard deviation is approximately 15. This can be determined by using the empirical rule, which states that for a normal distribution, about 68% of the values fall within one standard deviation of the mean, about 95% of the values fall within two standard deviations of the mean, and about 99.7% of the values fall within three standard deviations of the mean. Since 25% of the values are above 65, this means that 75% of the values are below 65. Therefore, the mean plus one standard deviation is 65, and the mean minus one standard deviation is 45. The standard deviation is therefore (65 - 45) / 2 = 10.

A Normal Distribution Has a Mean of 55, and About