Every Tuesday, Jason’s Video has “roll-the-dice” day. A customer may roll two fair dice and rent a second movie for an amount (in cents) determined by the numbers showing on the dice, the larger number first. For example, if the customer rolls a one and a five, a second movie may be rented for $0.51. Let x represent the amount paid for a second movie on roll-the-dice Tuesday.
a. Use the sample space for the rolling of a pair of dice and express the rental cost of the second movie, x, as a probability distribution.
b. What is the expected mean rental cost (mean of x) of the second movie on roll-the-dice Tuesday?
c. What is the standard deviation of x?
d. Using a computer and the probability distribution found in part a, generate a random sample of 30 values for x and determine the total cost of renting the second movie for 30 rentals.
e. Using a computer, obtain an estimate for the probability that the total amount paid for 30 second movies will exceed $15.00 by repeating part d 500 times and using the 500 results.