1. For a population with = 100 and = 20 what z score corresponds to a score of X = 120; X = 90; X = 125?

2. A student scores 74 on a test where the scores are normally distributed and mean score is 57 and the standard deviation is 17. What is the student's score when the distribution is rescaled to a mean of 50 and a standard deviation of 10?

3. A test is normally distributed with a mean of 60 and a standard deviation of 10. Based on the empirical rule, what proportion of the scores are above 80?

4. Based on the empirical rule find the proportion of cases are between minus two standard deviations and minus one standard deviation.

5. The 2013 SAT Verbal test had a mean score of 496 and a standard deviation of 115. ACT Critical Reading scores have a mean of 21.4 and a standard deviation of 6.2. Rose took both tests and scored 520 on the SAT and 24 on the ACT. Which test did Rose perform better compared to other students who took the same tests? Use the z table for your answer.

6. Diastolic blood pressure is normally distributed with a mean of 80 mm Hg and a standard deviation of 12. How would you classify someone whose diastolic blood pressure is above 116 based on the z score you calculated? Use the z table for your answer

7. On an IQ test with a mean of 100 and a standard deviation of 15, John's Z score is 1. 5. What is John's score on the IQ test?

8. In a chemistry mid-term exam Mary's score corresponds to a z score of 2. What percentage of students performed better than Mary? What percentage of students did Mary outperform?.

9. The most commonly used IQ test has a mean of 100 and a standard deviation of 15. Based on this test what percent of the population qualifies for membership in Mensa (to join you have to have an IQ of 130 or greater)?