Customers make purchases at a convenience store, on average, every six minutes. It is fair to assume that the time between customer purchases is exponentially distributed. Jack operates the cash register at this store. a. What is the rate parameter A? What is the standard deviation ofthis distribution? b. Jack wants to take a five-minute break. He believes that if he goes right after he has serviced a customer, he will lowerthe probability of someone showing up during his five-minute break. Is he right in this belief? c. What is the probabilitythat a customer will show up in less than five minutes? d. What is the probabilitythat nobody shows up for over half an hour? The mileage (in 1,000s of miles) that car owners get with a certain kind of radial tire is a random variable Y having a lognormal distribution such that Y = 6" where X is normally distributed. Let the mean and the standard deviation of the life of a radial tire be 40,000 miles and 5,000 miles, respectively. a. Compute the mean and standard deviation of X. b. What proportion of the tires will last for more than 50,000 miles? 0. What proportion of the tires will last for no more than 35,000 miles? (1. Compute the 95th percentile of the life expectancy of the tire