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25 September, 17:52

Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 16 seconds. Thus, 99.7% of running times are approximately between:

A. 61 and 125 seconds

B. 77 and 109 seconds

C. 45 and 141 seconds

D. None of the answer options is correct

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Answers (1)
  1. 25 September, 21:50
    0
    C. 45 and 141 seconds

    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 = 93 seconds

    Standard deviation = 16 seconds

    99.7% of running times are approximately between:

    By the Empirical rule, within 3 standard deviations of the mean, so between 3 standard deviations below the mean and 3 standard deviations above the mean

    3 stnadard deviations below the mean

    93 - 3*16 = 45 seconds

    3 standard deviations above the mean

    93 + 3*16 = 141 seconds

    The correct answer is:

    C. 45 and 141 seconds
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