Question

Math

Posted 4 months ago

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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: $\$ 110$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

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 \times 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).

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