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: The mean number of slices sold is 200, and the revenue per slice is $2, so the total mean revenue is $2 imes 200 = $400. The fixed costs are $160, so the mean profit is $400 - $160 = $240. ‖ ‖ step 2 ⋮ Calculate the standard deviation of the profit: The standard deviation of the number of slices sold is 25, and since the revenue per slice is $2, the standard deviation of the revenue is $2 imes 25 = $50. The fixed costs do not affect the standard deviation, so the standard deviation of the profit is also $50. ‖ ∻[question number] Answer∻ ***C*** ∻Key Concept∻ ⚹Linear Transformation of Random Variables⚹ ∻Explanation∻ ⚹When a random variable is multiplied by a constant (revenue per slice), its standard deviation is also multiplied by that constant. The mean of the random variable is affected by both multiplication and addition/subtraction (total revenue and fixed costs), but the standard deviation is not affected by addition/subtraction (fixed costs).⚹◊What is the formula for calculating the profit per event for the school selling pizza slices during sporting events?⍭ Generate me a similar question◊$

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