A school sells pizza slices at the concession stand during each sporting event. The school sells a mean of 200 slices per event with a standard deviation of 25 slices.

The school spends $\$ 160$ of fixed costs to buy the pizza before the event and earns a revenue of $\$ 2$ per slice. They calculate their profit per event according to this formula:
$$
\text { profit }=[\text { total revenue }]-[\text { total costs }]
$$

What will be the mean and standard deviation of the distribution of profit per event?
Choose 1 answer:
(A) Mean: $\$ 80$
Standard deviation: $\$ 50$
(B) Mean: $\$ 80$
Standard deviation: $\$ 110$
(C) Mean: $\$ 240$
Standard deviation: $\$ 50$
(D) Mean: $\$ 240$
Standard deviation: $\$ 110$

Question

A school sells pizza slices at the concession stand during each sporting event. The school sells a mean of 200 slices per event with a standard deviation of 25 slices.

The school spends $\$ 160$ of fixed costs to buy the pizza before the event and earns a revenue of $\$ 2$ per slice. They calculate their profit per event according to this formula:
$$
\text { profit }=[\text { total revenue }]-[\text { total costs }]
$$

What will be the mean and standard deviation of the distribution of profit per event?
Choose 1 answer:
(A) Mean: $\$ 80$
Standard deviation: $\$ 50$
(B) Mean: $\$ 80$
Standard deviation: $\$ 110$
(C) Mean: $\$ 240$
Standard deviation: $\$ 50$
(D) Mean: $\$ 240$
Standard deviation: $\$ 110$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the mean profit per event using the formula: profit = total revenue - total costs. The mean total revenue is the mean number of slices sold times the revenue per slice, which is $200 imes $2 = $400. The total costs are fixed at $160. Therefore, the mean profit is $400 - $160 = $240. ‖ ‖ step 2 ⋮ The standard deviation of profit depends only on the variable part of the profit, which is the total revenue since the total costs are fixed. The standard deviation of the total revenue is the standard deviation of the number of slices sold times the revenue per slice, which is $25 imes $2 = $50. ‖ ‖ step 3 ⋮ The mean and standard deviation of the distribution of profit per event are therefore $240 and $50, respectively. ‖ ***C*** ∻Key Concept∻ ⚹Linear Transformation of Random Variables⚹ ∻Explanation∻ ⚹When a random variable is multiplied by a constant, its standard deviation is also multiplied by that constant, while its mean is multiplied by the constant and then increased or decreased by any additional constant amount.⚹◊What is the formula for calculating profit per event in this scenario?⍭ Generate me a similar question◊

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