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28 October, 03:15

Peter has collected data to find that the finishing times for cyclists in a race has a normal distribution. Based on the Empirical Rule, what is the probability that a randomly selected race participant had a finishing time of greater than 171 minutes if the mean is 156 minutes and the standard deviation is 15 minutes? Enter your answer as a percent rounded to 2 decimal places if necessary. Include the percent symbol % in your answer.

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  1. 28 October, 05:50
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    16%

    Step-by-step explanation:

    Emperical rule states that:

    1. About 68% of data fall within 1 standard deviation of mean.

    2. About 95% of data falls within 2 standard deviation of mean.

    3. About 99.7% of data falls within 3 standard deviation of mean.

    Let the time to finish for cyclist be y

    P (y>156) = 1 - P (y < = 156)

    1 - P (y - u/6 < = 171 - 151)

    1 - P (z<=1)

    156 minutes falls within 1 standard deviation, above the mean the Probability of getting more than 156mins is

    1 - 0.68 / 2 = 0.16

    0.16 * 100=16%
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