When used in a particular DVD player, the lifetime of a certain brand of battery is normally distributed with a mean value of 6 hours and a standard deviation of 0.8 hour. Suppose that two new batteries are independently selected and put into the player. The player ceases to function as soon as one of the batteries fails.
a. What is the probability that the DVD player functions for at least 4 hours?
b. What is the probability that the DVD player functions for at most 7 hours?
c. Find a number x* such that only 5% of all DVD players will function without battery replacement for more than x* hours.