Suppose the distribution of tire wear for a radial brand of auto tire is approximately normal with a mean of 48,000 miles and a standard deviation of 2,000 miles. Find the probability of the tires which would be expected to wear in the following intervals an show the shaded region on the graph:
a. less than 46,000 miles
b. greater that 49,000 miles
c. between 47,000 miles and 51,000 miles
d. between 49,000 miles and 51,000 miles