Question

For an intramural sports program at a particular college, the time to run one mile is recorded for 200 male students in the program. These times are approximately normal with mean 8 minutes and standard deviation 1 minute. For the same intramural sports program at the same college, the time to run one mile is recorded for 50 female students in the program. These times are approximately normal with mean 7.5 minutes and standard deviation 2 minutes. Devon participates in the intramural program for men. His best time to run the mile is 6.6 minutes. Kendall participates in the intramural program for women. Her best time to run the mile is 5.7 minutes. Who ran the mile faster relative to their gender?

Answer 1

Answer:

Devon has the lower z-score, so he was faster relative to his gender.

Step-by-step explanation:

Z - score

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

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

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.

Who ran the mile faster relative to their gender?

Who runs in less time the mile is faster, so whoever has the lower z-score is faster relative to their gender.

Devon participates in the intramural program for men. His best time to run the mile is 6.6 minutes.

For men, these times are approximately normal with mean 8 minutes and standard deviation 1 minute.

So we have to find Z when $X = 6.6, \mu = 8, \sigma = 1$

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

$Z = \frac{6.6 - 8}{1}$

$Z = -1.4$

Kendall participates in the intramural program for women. Her best time to run the mile is 5.7 minutes.

For women, these times are approximately normal with mean 7.5 minutes and standard deviation 2 minutes.

So we have to find Z when $X = 5.7, \mu = 7.5, \sigma = 2$

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

$Z = \frac{5.7 - 7.5}{2}$

$Z = -0.9$

Devon has the lower z-score, so he was faster relative to his gender.