Instructions: Show all steps of your calculations for full credit. For word problems, answer in your own words. Please clearly indicate your final answer (e.g., by putting a box around it).

1. Suppose you discover that your annual salary, which is $5,000 below the mean salary in the population, translates to 0.5 standard deviations below the mean. What is the standard deviation in the population?

2. In one Sociology class, the distribution of the final exam scores has a mean of 74 and a standard deviation of 9. A student who took the exam scored 53. The student retook the class the following semester and scored 52 on a final exam that had a mean score of 70 and a standard deviation of 10. Use z-scores to determine if the student did better the second time around. Explain your answer.

3. You take a standardized test and you are told that the mean score on this test is= 400 with a standard deviation of= 100. You are told that your standardized score isz= 1.3. What is your score on the test?

4. Your friend takes the same test and is told that she scored 0.4 standard deviations below the mean. What is your friend's score?

5. On average, a used two-year-old Honda Civic sells for $11,835. Suppose you bought one for just $10,500. Which scenario would suggest that you got a better deal, one in which the standard deviation of the purchase price is $900, or when the standard deviation is $1,500? Usez-scores to answer this question.

6. CHALLENGE QUESTION (OPTIONAL): Suppose that you scored 60 on a test that has a population mean of 64 and a standard deviation of 8. If the population distribution were to be transformed into one with a mean of 50 and a standard deviation of 10, what would your score be in this new distribution?