Question

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?

Answer 1

Given that Sam'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