The Los Angeles Times (June 14, 1995) reported that the U.S. Postal Service is getting speedier, with higher overnight on-time delivery rates than in the past.

Postal Service standards call for overnight delivery within a zone of about 60 miles for any first-class letter deposited by the last collection time posted on a mailbox.

Two-day delivery is promised within a 600-mile zone, and three-day delivery is promised for distances over 600 miles. The Price Waterhouse accounting firm conducted an independent audit by “seeding” the mail with letters and recording on-time delivery rates for these letters.

Suppose that the results of the Price Waterhouse study were as follows (these numbers are fictitious, but they are compatible with summary values given in the article):

Number of Letters Mailed Number of Letters Arriving on Time Los Angeles 500 425 New York 500 415 Washington, D.C. 500 405 Nationwide 6000 5220 Use the given information to estimate the following probabilities:

a. The probability of an on-time delivery in Los Angeles

b. The probability of late delivery in Washington, D.C.

c. The probability that both of two letters mailed in New York are delivered on time

d. The probability of on-time delivery nationwide.