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8. The number of hurricanes hitting the coast of Florida annually has a Poisson distribution with a mean of 0.8. ( a) What is the probability that more than two hurricanes will hit the Florida coast in a year? ( b) What is the probability that exactly one hurricane will hit the coast of Florida in a year?
9. Arrivals at a bank teller’s drive- through window are Poisson- distributed at the rate of 1.5 per minute. ( a) What is the probability of zero arrivals in the next minute? ( b) What is the probability of zero arrivals in the next 2 minutes?
20. Suppose that a Die- Hardly- Ever battery has an exponential time- to- failure distribution with a mean of 48 months. At 60 months, the battery is still operating. ( a) What is the probability that this battery is going to die in the next 12 months? ( b) What is the probability that the battery dies in an odd year of its life? ( c) If the battery is operating at 60 months, compute the expected additional months of life.
25. The time intervals between hits on a web page from remote computers are exponentially distributed, with a mean of 15 seconds. Find the probability that the third hit connection occurs after 30 seconds have elapsed.