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14 April, 09:41

A random sample of adult female reaction times has a sample mean of x¯=394.3 milliseconds and sample standard deviation of s=84.6 milliseconds. Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.

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  1. 14 April, 10:22
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    The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.

    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 = 394.3 ms

    Standard deviation = 84.6 ms

    Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.

    140.5 = 394.3 - 3*84.6

    So 140.5 is 3 standard deviations below the mean.

    648.1 = 394.3 + 3*84.6

    So 648.1 is 3 standard deviations above the mean.

    By the Empirical Rule,

    The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.
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