In 2020, all salesman had average sales of $500,000 with a standard deviation of $100,000. Average sales and the standard deviation of sales across all salesmen are expected to be the same in 2021. 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 .25. Now consider salesperson Patty -- she had sales of $700,000 in 2020. Calculate the most appropriate prediction for Patty’s 2021 sales assuming a year-to-year correlation of .25?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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In 2020, all salesman had average sales of $500,000 with a standard deviation of $100,000. Average sales and the standard deviation of sales across all salesmen are expected to be the same in 2021. 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 .25.

Now consider salesperson Patty -- she had sales of $700,000 in 2020.

Calculate the most appropriate prediction for Patty’s 2021 sales assuming a year-to-year correlation of .25?

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