The mileage (in thousands 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 = ex 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?

c. What proportion of the tires will last for no more than 35.000 miles?

d. Compute the 95th percentile of the life distribution of the tire. LO5