9 November, 14:32

# When sam goes to a restaurant, he always tips the server \$2 plus 10% of the cost of the meal. if sam's distribution of meal costs has a mean of \$9 and a standard deviation of \$3, what are the mean and standard deviation of the distribution of his tips?

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1. 9 November, 17:28
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Given that S am's distribution of meal costs has a mean of \$9 and a standard deviation of \$3, this means that the range of Sam's meal cost that are within one standard deviation is given by (\$9 - 3, \$9 + 3) = (\$6, \$12).

Given that Sam always tips the server \$2 plus 10% of the cost of the meal, this means that when the cost of the meal is \$9, Sam tips \$2 + (0.1 x 9) = \$2 + \$0.9 = \$2.90

Therefore, the mean of the distribution of Sam's tips is \$2.90

Similarly, the range of Sam's tips that are within one standard deviation is given by (\$2 + 0.1 (6), \$2 + 0.1 (12)) = (\$2 + 0.6, \$2 + 1.2) = (\$2.6, 3.2) = (\$2.9 - \$0.3, \$2.9 + \$0.3)

Therefore, the standard deviation of the distribution of Sam's tips is \$0.3