A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down during the warranty period. Suppose an auto store makes a net profit of $20 on batteries that stay trouble-free during the warranty period; it makes a net loss of $10 on batteries that break down. The life of batteries is known to be normally distributed with a mean and a standard deviation of 40 and 16 months, respectively.
a. What is the probability that a battery will break down during the warranty period?
b. What is the expected profit of the auto store on a battery?
c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month?