Question

The heights of students in a class are normally distributed with mean 56 inches and standard deviation 4 inches. Use the Empirical Rule to determine the interval that contains the middle 68% of the heights.

Answer 1

The interval that contains the middle 68% of the heights is from 52 inches to 60 inches.

Explanation:

The empirical rule states that, for a normally distributed variable:

The middle 68% of the measures are within 1 standard deviation of the mean.

The middle 95% of the mesures are within 2 standard deviations of the mean.

The middle 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Normally distributed with mean 56 inches and standard deviation 4 inches.

So the interval that contains the middle 68% of the heights is from 52 inches to 60 inches.