Question

students applying to a certain military academy must take a fitness test. one component of the test has applicants complete as many sit - ups as possible in fixed amount of time. higher numbers of sit - ups are preferred, and the academy calculates the results separately for males and females. here are some summary statistics for the sit - ups portion of the fitness test:

gender	mean	standard deviation
female	$mu = 78$	$sigma = 5.7$

vitor (who is male) and manuela (who is female) both completed 80 sit - ups on the fitness test.

relative to their gender, who completed more sit - ups?

choose 1 answer:

Explanation:

Step1: Calculate Vitor's z - score

Use the z - score formula $z=\frac{x-\mu}{\sigma}$. For Vitor (male), $x = 80$, $\mu=81$, $\sigma = 4.7$. So $z_{Vitor}=\frac{80 - 81}{4.7}=\frac{-1}{4.7}\approx - 0.21$.

Step2: Calculate Manuela's z - score

For Manuela (female), $x = 80$, $\mu = 78$, $\sigma=5.7$. So $z_{Manuela}=\frac{80 - 78}{5.7}=\frac{2}{5.7}\approx0.35$.

Step3: Compare z - scores

Since $z_{Manuela}\approx0.35$ and $z_{Vitor}\approx - 0.21$, and a higher z - score means a better performance relative to the group, Manuela performed better relative to her gender.

Answer:

Manuela