Capital Car Wash sells a membership card for $25 per year that entitles the buyer to a $2 discount on each car wash purchased during the year. The number of times Danica washes her car has a mean of 15 with standard deviation of 4. What are the mean and standard deviation of the net gain Danica receives if she buys a membership card?

a. The mean of the net gain Danica receives if she buys a membership card is $5.

b. The standard deviation of the net gain Danica receives if she buys a membership card is $8.

Step-by-step explanation:

Price of a membership card per year = $25

Discount on each car wash purchased during the year = $2

Mean of the number of times Danica washes her car = 15

Standard deviation of the number of times Danica washes her car = 4

a. Calculation of the mean of the net gain Danica receives if she buys a membership card

Mean of the net gain = (Discount on each car wash purchased during the year * Mean of the number of times Danica washes her car) - Price of a membership card per year (1)

Substituting the values into equation (1), we have:

Mean of the net gain = ($2 * 15) - $25 = $30 - $25 = $5

b. Calculation of the standard deviation of the net gain Danica receives if she buys a membership card

Standard deviation of the net gain = Discount on each car wash purchased during the year * Standard deviation of the number of times Danica washes her car (2)

Substituting the values into equation (2), we have:

Standard deviation of the net gain = $2 * 4 = $8

Conclusion

The mean of the net gain Danica receives if she buys a membership card is $5, and the standard deviation of the net gain Danica receives if she buys a membership card is $8.