Problem #7: Each day, John performs the following experiment. He flips a fair coin repeatedly until he gets a 'T' and counts the number of coin flips needed. (a) Approximate the probability that in a (non-leap) year there are at least 3 days when he needed strictly more than 9 coin flips. (b) Approximate the probability that in a year there are strictly more than 32 days when he needed exactly 4 coin flips.Problem #5: Suppose that the distribution of the lifetime of a car battery produced by a certain car company is well approximated by a normal distribution with a mean of 1600 hours and variance 104. What is the approximate probability that a batch of 100 car batteries will contain at least 16 whose lifetimes are less than 1514 hours