Question

Suppose the heights of the members of a population follow a normal distribution. If the mean height of the population is 68 inches and the standard deviation is 4 inches, 95% of the population will have a height within which of the following ranges?

Answer 1

60 -76 is the range

Explanation:

As the graph shows, if we are in 2 standard deviations of the mean, we are in (34.1 + 13.6) *2 = 47.7*2 = 95.4 %

Our mean is 68

2 standard deviations is 2 * 4 = 8

68-8 = 60

68 * 8 = 76

We need to be between 60 and 76 to have at 95% confidence interval

Answer 2

The empirical rule states that at 95% the measurements would be within 2 standard deviations of the mean.

You are given a mean of 68 inches and a standard deviation of 4.

2 times the standard deviation = 2 x 4 = 8

So 95% of the heights would be between 68-8 = 60 inches and 68+8 = 76 inches.