The US Postal Service reports 95 of first class mail within

The US Postal Service reports 95% of first class mail within the same city are delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations.

a. What is the probability that all six arrive within 2 days?

b. What is the probability that exactly five arrive in 2 days?

c. Find the mean number of letters that will arrive within 2 days.

d. Compute the variance and the standard deviation of the number that will arrive within 2 days.

Solution

a. Probability that all six arrive within 2 days = (0.95)⁶ = 0.7351

b. Probability that exactly five arrive in 2 days = (6C5)(0.95)⁵(0.05) = 0.2321

c. mean number of letters that will arrive within 2 days. = n*p = 6*0.95 =5.7

d. variance of the number that will arrive within 2 days. = n*p*q = 6*0.95*0.05 =0.285

standard deviation of the number that will arrive within 2 days = 0.5339