Question: 3.78. For a sample with mean y, adding a constant c to each observation changes the mean to y + c, and the standard deviation

3.78. For a sample with mean y, adding a constant c to each observation changes the mean to y +

c, and the standard deviation s is unchanged. Multiplying each observation by c changes the mean to cy and the standard deviation to |c|s.

(a) Scores on a difficult exam have a mean of 57 and a standard deviation of 20. The teacher boosts allthe scores by20 points before awarding grades. Report the mean and standard deviation of the boosted scores.

(b) Suppose that annual income of Canadian lawyers has a mean of $100,000 and a standard deviation of $30,000. Values are converted to

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