There are three questions related to this problem.
First, the probability of the mail will arrive after 2:30
PM
Find the z-score of 2:30 which is 30 minutes after 2:00.
z(2:30) = (2:30 – 2:00)/15 = -30/15 = -2
P(x < 2:30) = P(z<-2) = 0.0228
Second, the probability of the mail will arrive at 1:36
PM
Find the z-score of 1:36 which is 24 minutes before 2:00.
z(1:36) = (1:36 – 2:00)/15 = -24/15 = -1.6
P(x < 1:36) = P(z<-1.6) = 0.0548
Lastly, the probability of the mail will arrive between 1:48
PM and 2:09 PM
Find the z-score of 1:46 and 2:09 PM which will result to
a z value of 0.034599
P(1:48 < x < 2:09) = P(z<0.034599) = 0.5138
