Joan’s finishing time for the Bolder Boulder 10K race was 1.76 standard deviations faster than the women’s average for her age group. There

Question

Joan’s finishing time for the Bolder Boulder 10K race was 1.76 standard deviations faster than the women’s average for her age group. There were 420 women who ran in her age group. Assuming a normal distribution, how many women ran faster than Joan?

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Rylee 2 months 2021-10-18T17:21:45+00:00 1 Answer 0 views 0

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    2021-10-18T17:23:32+00:00

    Answer:

    16 women ran faster than Joan

    Step-by-step explanation:

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

    Joan’s finishing time for the Bolder Boulder 10K race was 1.76 standard deviations faster than the women’s average for her age group.

    This means that Z = 1.76

    Z = 1.76 has a pvalue of 0.9608.

    So Joan’s was faster than 96.08% of the runners and slower than 3.92% of the runners

    0.0392*420 = 16

    16 women ran faster than Joan

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