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.

Question

Mathematics

Kayla Kim

31 October, 11:39

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.

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Robert Gaines · Answer 1

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

Step-by-step 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.