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.

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?