Question

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?

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 $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• 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:

$\mu = 22.5, \sigma = 2$.

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:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{25 - 22.5}{2}$

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.

More can be learned about the normal distribution at https://brainly.com/question/24663213