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4 May, 17:45

In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 2.5 inches. Using the empirical rule, determine the interval of heights that represents the middle 95% of male heights from this school.

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  1. 4 May, 18:04
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    Answer: the interval of heights that represents the middle 95% of male heights from this school is between 66 inches and 76 inches.

    Step-by-step explanation:

    Let x be a random variable representing the heights of males from this school. With the mean and standard deviation given, then the Empirical Rule says the that

    1) About 68% of the x values lie between 1 standard deviation below and above the mean.

    2) About 95% of the x values lie between 2 standard deviations below and above the mean.

    3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.

    From the information given,

    mean = 71 inches

    Standard deviation = 2.5 inches

    We want to determine where 95% of x values lies. This is 2 standard deviations from the mean Therefore,

    2 standard deviations = 2 * 2.5 = 5 inches

    The heights are

    71 - 5 = 66 inches and

    71 + 5 = 76 inches
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