67. 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 ll? 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 fiveminute break. Is be right in this belief? c. What is the probability that a customer will show up in less than five minutes? d. What is the probability that nobody shows up for over half an hour? 51. (Use Excel) While Massachusetts is no California when it comes to sun, the solar energy industry is flourishing in this state (The Boston Globe, May 27, 2012). The state's capital, Boston, averages 211.7 sunny days per year. Assume that the number of sunny days follows a normal distribution with a standard deviation of 20 days. In addition to providing the answer, state the relevant Excel commands. a. What is the probability that Boston has less than 200 sunny days in a given year? b. Los Angeles averages 266.5 sunny days peryear. What is the probability that Boston has at least as many sunny days as Los Angeles? c. Suppose a dismal year in Boston is one where the number of sunny days is in the bottom 10% forthat year. At most, how many sunny days must occur annually for it to be a dismal year in Boston? d. In 2012, Boston experienced unusually warm, dry, and sunny weather. Suppose this occurs only 1% of the time. What is the minimum number of sunny days that would satisfy the criteria for being an unusually warm, dry, and sunny year in Boston