A cell phone company offers a simple extended warranty plan. If your phone is damaged, they will repair it for up to $50. If you lose or destroy your phone, they will give you a $200 voucher towards a new phone. The company believes that 5% of customers will need the replacement voucher and 10% will request a repair.
a.) If the company charges $25 for this extended warranty, what is the expected value of the profit they will earn?
b.) What is the standard deviation of their profit?
c.) Suppose the company collects 10 warranty plans on one day. What is the mean of the company’s total profit?
d.) What is the standard deviation of the 10 warranty plans?
e.) What are the mean and standard deviation for the profit on a 1000 plans?
f.) What do your answers to the previous question tell you about the company’s likelihood of making a profit?
g.) Is the $25 warranty a wise purchase for you? Given that you will probably buy dozens of devices over the next decade, are these types of warranties a wise purchase for you?
