When sam goes to a restaurant he always tips the server $2 plus 10% of the cost of the meal is sams distribution of meal costs has a mean of $9 and a standard deviation of $3 what are the mean and standard deviation of of the distribution of his tips?

Question

Advanced Placement (AP)

Alanna Mason

17 July, 20:24

When sam goes to a restaurant he always tips the server $2 plus 10% of the cost of the meal is sams distribution of meal costs has a mean of $9 and a standard deviation of $3 what are the mean and standard deviation of of the distribution of his tips?

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Answers (1)

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Kelvin Nichols · Answer 1

Given tip, T = $2.00 + (0.1 X C)

where C = cost of meal

Mean of cost of meals, M = $9.00

Standard deviation of meal, Sm = $3.00

If C = M,

Mean of tips Mt = $2.00 + (0.1 X $9.00)

Mt = $2.90, mean of tips

Standard deviation of tips, St = square root of mean of tips

St = ($2.90) ^0.5

St = $1.70, standard deviation of tips

Therefore, mean of tips = $2.90 and standard deviation of tips = $1.70