5.24 The tread life of Road Stone tires has a normal distribution with a mean of 35,000 miles and a standard deviation of 4,000 miles.

a. What proportion of these tires has a tread life of more than 38,000 miles?

b. What proportion of these tires has a tread life of less than 32,000 miles?

c. What proportion of these tires has a tread life of between 32,000 and 38,000 miles?

d. Draw a graph of the probability density function of tread lives, illustrating why the answers to parts (a)

and

(b) are the same and why the answers to parts

(a), (b), and

(c) sum to 1.