12. Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was

approximately normal with mean 259 minutes and standard deviation 32 minutes. The distribution of finishing time for

men was approximately normal with mean 242 minutes and standard deviation 29 minutes.

(a) The finishing time for Clay was 289 minutes. Calculate and interpret the standardized score for Clay's marathon

time. Show your work.

B. (b) The finishing time for Kathy was 272 minutes. What proportion of women who ran the marathon had a finishing

time less than Kathy's? Show your work.

C. (c) The standard deviation of finishing time is greater for women than for men. What does this indicate about the

finishing times of the women who ran the marathon compared to the finishing times of the men who ran the

marathon?

13. No matter what the scores are on the SAT every year, the entire data set for each section is transformed so that the mean

is 500 points with a standard deviation of 100 points. Assume that this year, the mean of all student scores was 510 and

the standard deviation was 120. Write a transformation in the form y = ax + b where represents this years score and y

represents the transformed score, Show work.

a=

b=