The U.S. Postal Service reports 95% of first-class mail within the same city is 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 within 2 days?
c. Find the mean number of letters that will arrive within 2 days.
d. Compute the variance and standard deviation of the number that will arrive within 2 days.