A gym class is taking a fitness test. The gym teacher is recording how many sit-ups the par- ticipants can do in a minute. The count for the population is normally distributed, with a mean of 36 sit-ups and a standard deviation of 4 sit-ups. Mason's z-score is 2 and Jamal's is -1. How many more sit-ups did Mason do than Jamal?

Formula for Z score ,
Z score = $\frac{\mathrm{score} - \mathrm{mean}}{\mathrm{standard} \mathrm{deviation}}$

Therefore, $\mathrm{score} = \mathrm{mean} +\hspace{0.17em}\mathrm{Z} \mathrm{score} *\hspace{0.17em}\mathrm{standard} \mathrm{deviation}$

Here, mean, µ = 36

standard deviation, σ = 4

Mason's Z score of sit ups = 2

Hence, the number of sit ups Mason does = $\mathrm{mean} +\hspace{0.17em}\mathrm{Z} \mathrm{score} *\hspace{0.17em}\mathrm{standard} \mathrm{deviation} = 36+2*4 = 44$

Jamal's Z score of sit ups = -1

Hence, the number of sit ups Jamal does = $\mathrm{mean} +\hspace{0.17em}\mathrm{Z} \mathrm{score} *\hspace{0.17em}\mathrm{standard} \mathrm{deviation} = 36+(-1)*4 = 32$