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Sonja
2 months ago
7

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 cost

s has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of the distribution of his tips?
Business
1 answer:
soldi70 [3.6K]2 months ago
5 0
Sam's meal costs have an average of $9 with a standard deviation of $3, so the meal costs lying within one standard deviation range from $6 to $12 ($9 - 3 to $9 + 3).

Since Sam tips $2 plus 10% of the meal price, for a $9 meal he tips $2 + 0.1 × 9 = $2.90.

Thus, the average tip amount is $2.90.

The tip amounts that fall within one standard deviation correspond to meals priced between $6 and $12, meaning the tips range from $2 + 0.1×6 = $2.60 to $2 + 0.1×12 = $3.20. This matches the interval ($2.90 - $0.30, $2.90 + $0.30).

Hence, the standard deviation for the tip amounts is $0.30.
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