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Brenda has collected data to find that the finishing times for cyclists in a race has a normal distribution. What is the probability that a randomly selected race participant had a finishing time of greater than 154 minutes if the mean is 143 minutes and the standard deviation is 11 minutes? Use empirical rule. Provide final answer as a percent.

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ashleycarter707

Answer: 16%

Step-by-step explanation:

Notice that 154 minutes is one standard deviation greater than the mean. Based on the empirical rule 68% of the finishing times are within one standard deviation of the mean, so 100%-68%=32% of the finishing times are outside of one standard deviation from the mean one either direction. Since the normal distribution is symmetric , half of the 32% will be less than the mean and half will be greater, so 16% of the finishing times are greater than the one standard deviation more than the mean.

raphealnwobi

The probability that race participant had a finishing time of greater than 154 minutes is 16%

The empirical rule states that for a normal distribution, 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are are within three standard deviation from the mean.

Given that mean (μ) = 143, standard deviation σ = 11

  1. 68% are within one standard deviation = μ ± σ = 143 ± 11 = (132, 154)

The probability that race participant had a finishing time of greater than 154 minutes is 16% [(100% - 68%)/2]

Find out more at: brainly.com/question/12660012

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