12. Find the mean and variance of the binomial random variable of b(x;15,0.4), and then use Chebyshev's theorem to interpret the interval a # 20. 13. For a certain manufacturing process, it is known that, on the average, 1 in every 100 items is defective. What is the probability that the fifth item inspected is the first defective item found ? 14. In an NBA (National Basketball Association ) championship series , the team that wins four games out of seven is the winner . Suppose that teams A and B face each other in the champi - onship games and that team A has probability 0.55 of winning a game over team B. (a) What is the probability that team A will win the series in 6 games ? (b) What is the probability that team A will win the series ? (c) If teams A and B were facing each other in a regional playoff series, which is decided by winning three out of five games , what is the probability that team A would win the series ? 15. During a laboratory experiment , the average number of radioactive particles passing through a counter in 1 millisecond is 4. What is the probability that 6 particles enter the counter in a given millisecond? 16. On the average, 1 computer in 800 crashes during a severe thunderstorm. A certain company had 4,000 working computers when the area was hit by a severe thunderstorm. (a) Compute the probability that less than 10 computers crashed . (b) Compute the probability that exactly 10 computers crashed