Question

The distribution of the heights of students in a large class is roughly bell-shaped. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to:_______

a. 2
b. 3
c. 6
d. 9
e.12

Answer 1

Answer: a. 2

Explanation:

According to the Empirical rule, when data is normally distributed then 95% of the lies within 2 standard deviations from mean.

Given: The distribution of the heights of students in a large class is roughly bell-shaped ( i.e. Normally distributed).

The average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches.

Then, by Empirical rule, 68 -2(standard deviations) =62 [lower limit]

⇒ 2(standard deviations)= 68-62 = 4

⇒ standard deviations=2

Hence, correct option is a. 2

Answer 2

B-3

Explanation:

According to the empirical rule, roughly 95% of the distribution is within 2 standard deviations of the mean.

The mean is 68. The distance from 62 to 68 is 6 inches

68-62=6

Cut that in half to get 6/2 = 3

So the standard deviation is 3