The time at which the mailman delivers the mail to Ace Bike

The time at which the mailman delivers the mail to Ace Bike Shop follows a normal distribution with mean 2:00 PM and standard deviation of 15 minutes.

What is the probability the mail will arrive before 1:36 PM?

What is the probability the mail will arrive between 1:48 PM and 2:09 PM?

Solution

Data:

mean : 14:00 hour and 840 minutes if you multiplied 60*14 becouse it is necessary work with minutes, or all with the same unit

standard deviation: 15 min

a) P<= 13.36 hours , 13= 780+36 =816

x=816 z= (816-840)/(15) =-1.6 so the probability P=>-1.6 is = 0.0548

b) 13:48<= P=> 14:9

828<= P=> 849

x=828 z= (828-840)/(15) =-0.8 so the probability P=>-0.8 is = 0.2119

x=849 z= (849-840)/(15) =0.6 so the probability P=>0.6 is = 0.2743

so the probability (828<= P=> 849)=0.2743-0.2119 =0.0624, take into account the probability of positive Z to right wing and if the number is negative to the left