The Weekly Standard is a politically conservative magazine (and website), described in ads as humorous and witty. This magazine is read by some of the most powerful men and women in government, politics, and the media. According to a survey conducted by magazine staff, the mean amount spent during the past 12 months for personal or vacation travel is $6159. Suppose the distribution of the amount spent by a subscriber during the past 12 months for personal or vacation travel can be modeled by an exponential random variable.
a. Find the value of l.
b. Find the probability that a randomly selected subscriber spent more than $8000 for personal or vacation travel during the past 12 months.
c. Find the probability that a randomly selected subscriber spent between $5000 and $10,000 for personal or vacation travel during the past 12 months.
d. If a subscriber spent less than $500 for personal or vacation travel during the past 12 months, the circulation department will no longer hand-deliver each issue. What is the probability that a randomly selected subscriber will no longer receive hand-delivered issues?
The purpose of an automobile’s timing belt is to provide a connection between the camshaft and the crankshaft. This allows the valves to open and close in sync with the pistons. Suppose the duration of a timing belt (in miles) can be modeled by an exponential random variable with mean 100,000 miles.
a. Find the value of l.
b. Find the probability that a randomly selected timing belt lasts for more than 120,000 miles.
c. Find the probability that a randomly selected timing belt lasts for between 75,000 and 125,000 miles.
d. If the timing belt on a new car breaks within 70,000 miles, the dealer will install a new belt free of charge. What is the probability the dealer will be forced to install a new timing belt free of charge on a randomly selected car?