The lifetime of a certain brand of battery is normally distributed with a mean value of 9 hr and a standard deviation of 0.8 hr when it is used in a particular DVD player. Suppose that two new batteries are independently selected and put into the player. The player stops functioning as soon as one of the batteries fails. (Round your answers to four decimal places.) Required:
a. What is the probability that the player functions for at least 8 hr?
b. What is the probability that the cassette player works for at most 11 hr?
c. Find a number z* such that only 10% of all cassette players will function without battery replacement for more than z* hr.