Part a)
The finishing times for men followed an approximately normal distribution with a mean of 242 minutes and a standard deviation of 29 minutes.
We need to evaluate and interpret the standardized score for Clay's marathon time of 289 minutes.
The relevant formula is:

Inserting the values yields:


This indicates that Clay's marathon time is 1.62 standard deviations higher than the average finishing time.
Part b)
In this instance, the women's finishing times also displayed an approximate normal distribution, with a mean of 259 minutes and a standard deviation of 32 minutes.
We aim to determine the percentage of women completing the marathon in a time shorter than Kathy's, who finished in 272 minutes.
We first need to calculate the z-score:

According to the standard normal distribution table, P(z<0.41)=0.6591.
This indicates that 65.91% of female participants had a finishing time less than that of Kathy.
Part c
The standard deviation measures the extent of deviation of individual data points from the mean.
A higher standard deviation for women’s finishing times compared to men suggests that women’s finishing times are more spread out from the average than those for men.