The finishing times of a 5k race run by competitive male runners age 15-18 are approximately normal distribution with a mean time of 18 minutes and a standard deviation of 2 minutes. a particularly tough 5k race tends to take these same runners 4.5 additional minutes. to earn a completion medal in this particular 5k race, the runner must complete the race within 25 minutes. approximately, what percent of competitive male runners in the 15-18 age bracket typically do not earn a completion medal at this race?

Answers

Answer 1

Using the normal distribution, it is found that 0.1056 = 10.56% of runners do not earn the competition medal.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, considering the 4.5 additional minutes, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 22.5, \sigma = 2[/tex].

Runners that take more than 25 minutes to complete the race do not earn a medal, hence the proportion is one subtracted by the p-value of Z when X = 25, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{25 - 22.5}{2}[/tex]

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

1 - 0.8944 = 0.1056.

0.1056 = 10.56% of runners do not earn the competition medal.

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Answer:

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Answer:

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Explanation:

Answer:

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I hope this helps

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I’m sorry I didn’t understand the question you were trying to get answered. Please give the options and I can try to help you! Thank you.

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you are missing a part of the question i believe?

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