Which student got better marks in the examination?

Question

Jack and Jill study in different section of the same class. On a recent exam, Jack scored 98 out of 100 while Jill scored 97 out of 100. However, we know that in Jack's section the mean score was 80 with a standard deviation of 5, while in Jill's section the mean score was 82 with a standard deviation of 4. The scores in each section are normally distributed. Relative to each one's section, which student did better on the exam?

Answer 1

I would suggest calculating the $z$ score for each student where $$ z=\frac{x-\mu}{\sigma} $$ $\mu $ is the mean and $\sigma $ is the standard deviation. The student with the largest $z$ has performed, relative to the mean and measured in units of standard deviation, the best.