Question

Problem 11. (5 points) Roberto finishes a triathlon in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in 79.3 minutes. Among all women in the race, the mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. Who did better in relation to their gender?

Answer 1

11

part a

This is a normal distribution question with
$\\Mean (\mu)= 69.4 \\Standard\;Deviation (\sigma)= 8.9 \\Since\; we\; know\; that \\z_{ score } = \frac{x-\mu}{\sigma}$

P(x < 63.2)=?
The z-score at x = 63.2 is,
$z = \frac{63.2-69.4}{8.9} = -0.6966$
This implies that
$P(x < 63.2) = P(z < -0.6966) = \textbf{0.24302657792968957}$
PS: you have to refer z score table to find the final probabilities.

part b

This is a normal distribution question with
$\\Mean (\mu)= 84.7 \\Standard\;Deviation (\sigma)= 7.4 \\Since\; we\; know\; that \\z_{ score } = \frac{x-\mu}{\sigma}$

P(x < 79.3)=?
The z-score at x = 79.3 is,
$z = \frac{79.3-84.7}{7.4} = -0.7297$
This implies that
$P(x < 79.3) = P(z < -0.7297) = \textbf{0.2327867905631243}$
PS: you have to refer z score table to find the final probabilities.

Roberto did better than Zandra