3. A researcher investigates the speed with which a random sample of 50 participants completes a test. She obtains a sample mean of 136.42 minutes. For the population of people who have taken this test, the mean is 130 and the standard deviation is 18. i. What percentage of the time can she expect to obtain a sample mean of 136.42 or above? (4 points). ii. Explain why she obtained such an unusual x. (2 points).

4. A teacher finds that for test grades in Class A, x=32 and S x = 4; for test grades in Class B, x=32 and S x = 8. i. What score should he predict for students in each class? (1 point). ii. Which class permits the better predictions? Why? (2 points).

5. A researcher investigates whether daily exercise alters long-term stress levels. For a sample of 10 participants who exercised daily for two weeks, the researcher obtained the following stress scores:

40 59 48 36 44 43 45 45 32 37

i. Calculate and interpret the range. (1 points). ii. Calculate and interpret the variance. (3 points). iii. Calculate and interpret the standard deviation. (2 points).