2) When someone defaults on their rent on a storage unit, the unit may go up for auction so the owner can recoup some of the lost rent. The average auction price for a storage unit is $425 with a standard deviation of $45.

a) Theoretically, if you were to repeatedly select samples of 36 auctioned storage units and surveyed their auction prices, what would the average of all the sample means be?

b) How much error would you expect, on average, between the sample mean and t

3) The central limit theorem describes various properties of the sampling distribution of the mean, including its shape. For each of the following examples, indicate whether or not it can or cannot be assumed that the sampling distribution of the mean is normal, according to the central limit theorem.

a) The original population distribution is positively skewed andn= 9. Yes? Or No?

b) The original population distribution is negatively skewed andn= 14. Yes? or No?

c) The original population distribution is normal andn= 15. Yes? or No?

d) The original population distribution is uniform andn= 80. Yes or No?

4) Suppose you are administering a test that has a population standard deviation of= 80. You wish to have a standard error in your sample that is 10 points. What is the sample size you need?

5) Aubrey and Mindy are twins who are attending different colleges. They both took a biology class. In Aubrey's class, the mean percentage score was 82 with a standard deviation of 9, and she scored 75. In Mindy's class, the mean percentage score was 78 with a standard deviation of 10, and she scored 72.

a) Who did better in their biology class, Aubrey or Mindy? Usez-scores to find out.3

b) Mindy's classmate, Jeni, scored 1.8 standard deviations above the mean. What was Jeni's score?

c) Leo, another one of Mindy's classmates, scored in the 15thpercentile, which means his score was higher than 15% of the scores. What was Leo's score?

d) What proportion of students who took Mindy's class got an A (i.e., scored between 90 and 100?

e) What proportion of students who took Mindy's class got a C (i.e., scored between 70 and 79)?

f) What is the probability that a random sample of 4 students from Mindy's class would have a mean grade in the failing range (i.e., score below 60)?

6) A distribution has a standard deviation of 11. What is thez-score for a raw score that is 33 points above the mean?

7) For a normal distribution, what z-score values form the boundaries that separate the middle 10% of the distribution from the rest of the scores?

8) Two teams of researchers administered the same life satisfaction survey to adults in the United States. Team A surveyed a random sample of 750 adults and found that the average life satisfaction rating on an 10-point scale was 5.61. Team B surveyed a different random sample of 1,400 adults and found an average life satisfaction rating of 5.82. Theoretically, which team's average would you expect to be closer to the true average rating of life satisfaction? Explain your answer.