An unprincipled used-car dealer sells a car to an unsuspecting buyer, even though the dealer knows that the car will have a major breakdown within the next 6 months. The dealer provides a warranty of 45 days on all cars sold. Let x represent the length of time until the breakdown occurs. Assume that x is a uniform random variable with values between 0 and 6 months.

a. Calculate and interpret the mean and standard deviation of x.

b. Graph the probability distribution of x, and show the mean on the horizontal axis.

Also show one- and two-standard-deviation intervals around the mean.

c. Calculate the probability that the breakdown occurs while the car is still under warranty.