Questions 1-3 deal with the following information:

At American Widgets in 2020, across salespeople the average annual sales was $500,000, with a standard deviation of $100,000. Assume that a given salesperson's sales are positively but imperfectly correlated from one year to the next; in the past, year-to-year correlations have been about .5. Also, suppose that average sales (and the standard deviation in sales) across salespeople are expected to be the same in 2021 as they were in 2020. (That is, assume the 2021 overall average will be $500,000 and the 2021 standard deviation will be $100,000.)

Now consider salesperson Patty O'Furniture -- she had a quite good year in 2020, with $700,000 in sales.

1. (3 pts) Which of the following predictions of Patty's 2021 sales would best illustrate the concept of "prediction-by-evaluation"?

1. (a) $300,000 (f) $550,000
2. (b) $350,000 (g) $600,000
3. (c) $400,000 (h) $650,000
4. (d) $450,000 (i) $700,000
5. (e) $500,000 (j) $750,000

Please explain your answer, and describe the intuitive basis of such a prediction. (That is, how might someone making this prediction explain or justify it?)

2. (4 pts) Based on the information available, which of the following would be the most appropriate (i.e., normative) prediction for Patty's 2021 sales?

1. (a) $300,000 (f) $550,000
2. (b) $350,000 (g) $600,000
3. (c) $400,000 (h) $650,000
4. (d) $450,000 (i) $700,000
5. (e) $500,000 (j) $750,000

Describe your logic and show your work. (Hint: If you're having difficulty here, you may want to consider the method sketched out in Ch 18 of Kahneman's book.)

3. (3 pts) Suppose that the year-to-year correlation in sales was .25 rather than .5. How would this change the most appropriate prediction for Patty's 2021 sales; would the prediction increase, decrease, or stay the same (compared to the answer to question 2)? Calculate the most appropriate prediction for Patty's 2021 sales assuming a year-to-year correlation of .25. Describe your logic and/or show your work.