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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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  1. 31 October, 13:30
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    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.
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