60 students were given a history exam. Their scores were normally distributed with a mean of 75.5 and standard deviation of 11.9. The original scores are shown in the table. A.) If a student earns a score of 88, what is the z-score for this raw score?

B.) What is the percent of the scores above and below 88? Write as a percent rounded to 1 decimal place.

C.) What percent of the exam scores are between 70 and 90?

D.) What score would a student have earned if there z-score was 1.4?

E.) What score would a student have to earn to be in the 80th percentile?

F.) Now Consider both John and Mary both took tests on the same day. John took a history test in the class above and Mary took a math test. John scored an 85 on the history test in the class above and his sister Mary took a math test and scored 81.

Now if it was known that the distribution of the math grades was also normally distributed with a mean of 76 and standard deviation of 2, who scored better in comparison to their class? It appears John’s has a higher overall raw score, but who did better with respect to their class? How do you know?