Question

Consider the chance experiment in which a customer of an ice cream shop is randomly selected. Let x be the number of gallons of ice cream purchased. Suppose that the average amount of ice cream sold per customer is 2 gallons and the standard deviation is 0.7 gallons. The shop charges 5 dollars per gallon of ice cream and a service fee of 50 cents. Let y be the dollar amount a customer pays. a. Express y as a linear function of x. b. What are the mean and standard deviation of y?

Answer 1

Given,

x : Number of Gallons of Ice cream purchased a customer

Average amount of icecream sold per customer : Average number of gallons of icecream purchased by a customer : E(x) = 2 Gallons

Standard deviation of x = 0.7 gallons

y : the dollar amount a customer pays

The shop charges 5 dollars per gallon of ice cream and a service fee of 50 cents.(0.50 Dollors)

i.e y = 5 x Number of Gallons of Ice cream purchased by a customer + 0.50 = 5x + 0.50

y = 5x + 0.50

if y = ax + b ; then

Standard deviation of y =

Standard deviation of y = a x standard deviation of x

therefore

E(y) = 10.50 dollors

Mean of y = 10.50 dollors

Standard deviation of y = 5 x standard deviation of x = 5 x 0.7 = 3.5