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- Suppose that the service life in hours of a semicon-ductor is a random variable having a Weibull distribution (see Exercise 23) with α = 0.025 and β = 0.500.(a) How long can such a semiconductor be expectedto last?(b) What is the probability that such a semiconductor willstill be in operating condition after 4,000 hours?A newspaper editor finds that the average number of typographical errors perpage of the newspaper is 4. Assuming that the number of errors per page of that newspaper follows a Poisson distribution, determine the probability that on a given page thenumber of errors is greater than 2.A certain kind of sheet metal has, on average, 5 defects per 15 square feet.Assuming a Poisson distribution, find the probability that a 20 square foot metal sheet has at least 9 defects. Round your answer to four decimals.
- A manufacturing company claims that the number of machine breakdowns follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time (in hours0 between successive breakdowns. assuming that the manufacturing company's claim is true, find the probability that the time between successive breakdowns is at most five hours.Workers at Lyman Limited arrive at work at an average rate of 8 workers per hour. Assuming the arrival times follow a Poisson distribution, calculate the probability that a manager will observe: a) exactly 6 workers arriving in a given hour. b) at least 2 workers arriving in a 15-minute period.