Question

1. Suppose the expected number of customers entering a department store between 9 AM and 10 AM is 60.

a. What is the probability that exactly 1 customer enters between 9:00 and 9:01 ?

b. What is the probability that exactly 2 customers enter between 9:00 and 9:02 ?

c. What is the probability that exactly 2 customers enter between 9:00 and 9:01 GIVEN THAT exactly two customers enter between 9:00 and 9:02?

Answer 1

a)

expected number of customer in 1 minutes between 9:00 and 9:01 =1*60/60 =1

P( exactly 1 customer enters between 9:00 and 9:01 )=e^-11¹/1! =0.3679

b)

expected number of customer in 2 minutes between 9:00 and 9:02 =2*60/60 =2

P( exactly 2 customer enters between 9:00 and 9:02 )=e^-22²/2! =0.2707

c)

P( exactly 2 customers enter between 9:00 and 9:01 GIVEN THAT exactly two customers enter between 9:00 and 9:02 )

=P(2 between 9:00 and 9:01 and none between 9:01 and 9:02)/exactly 2 customer enters between 9:00 and 9:02 )

=(e^-11²/2!)*(e^-11⁰/0!)/(e^-22²/2!)

=0.1839*0.3679/0.2707

=0.25