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28 August, 21:54

uppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.2 and a standard deviation of 1.49. Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67

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  1. 28 August, 22:49
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    99.85% of American women have shoe sizes that are less than 12.67

    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 = 8.2

    Standard deviation = 1.49

    Using the empirical rule, what percentage of American women have shoe sizes that are less than 12.67

    12.67 = 8.2 + 3*1.49

    12.67 is 3 standard deviations above the mean.

    Since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above. Of those 50% above, 99.7% are between the mean and 12.67. So

    0.5 + 0.997*0.5 = 0.9985

    99.85% of American women have shoe sizes that are less than 12.67
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