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: profit=[total revenue]-[total cos ts] What will be the mean and standard deviation of the distribution of proft per event?

A. Mean: $80 Standard deviation: $50
B. Mean: $80 Standard deviation: $110
C. Mean: $240 Standard deviation: $50
D. Mean: $240 Standard deviation: $110

Answer 1

The mean and standard deviation of the distribution of profit per event can be calculated using the given information. The mean is $240 and the standard deviation is $50. The correct answer is Option C.

Step-by-step explanation:

The mean and standard deviation of the distribution of profit per event can be calculated using the given information. The formula for profit is profit = total revenue - total costs.

1. To calculate the mean of the distribution of profit per event, we need to calculate the mean of the total revenue and the mean of the total costs. The mean of the total revenue is the mean number of pizza slices sold per event multiplied by the revenue per slice, which is $2. Therefore, the mean of the total revenue is 200 slices/event * $2/slice = $400/event. The mean of the total costs is the fixed cost of $160/event.
2. Substituting the mean values into the profit formula, we get profit = $400/event - $160/event = $240/event.
3. To calculate the standard deviation of the distribution of profit per event, we can use the formula for combining independent random variables. The standard deviation of the total revenue is found by multiplying the standard deviation of the number of pizza slices sold per event by the revenue per slice, which is 25 slices/event * $2/slice = $50/event. The standard deviation of the total costs is 0 since it is a fixed cost. Substituting the standard deviation values into the formula, we get the standard deviation of the distribution of profit per event as $50/event.

Therefore, the mean and standard deviation of the distribution of profit per event are Mean: $240 and Standard deviation: $50, so the correct answer is Option C.