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28 September, 13:33

The distribution of the number of hours of sleep people get per night is unimodal and symmetric with a mean of 6 hours and a standard deviation of 1.5. Using the Empirical Rule, approximately what percentage of people sleep between 6 and 7.5 hours per night

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  1. 28 September, 13:58
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    Approximately 34% of people sleep between 6 and 7.5 hours per night

    Step-by-step explanation:

    The Empirical Rule states that, for a normally distributed random variable:

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

    95% of the measures are within 2 standard deviation of the mean.

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

    In this problem, we have that:

    Mean = 6

    Standard deviation = 1.5

    The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

    What percentage of people sleep between 6 and 7.5 hours per night

    6 is the mean.

    7.5 is 1 one standard deviation above the mean.

    By the Empirical Rule, of the 50% of the measures that are above the mean, 68% are within 1 standard deviation of the mean (between 6 and 7.5).

    0.5*0.68 = 0.34

    Approximately 34% of people sleep between 6 and 7.5 hours per night
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