Question

The number of customers arriving at a local business every 15 minutes is 3.  Supposing the arrival of customers follows a Poisson distribution, answer the following questions:

What is the probability that exactly 5 people arrive in the next 15 minutes?

What is the probability that at least 4 people arrive in the next 15 minutes?

Probability that between 2 and 6 people arrive inclusive?

Expected number to arrive in the next hour?

Expected number to arrive in an 8 hour day?

Answer 1

Ans:

P(x=5)=e^-3*(3^5/5!)=0.1008

P(at least 4)=P(x>=4)=1-P(x<=3)

=1-e^-3*(3⁰/0!+3¹/1!+3²/2!+3³/3!)

=1-e^-3*(1+3+4.5+4.5)=0.3528

P(2<=x<=6)=e^-3*(3²/2!+3³/3!+3⁴/4!+3⁵/5!+3⁶/6!)

=0.7673

Expected number to arrive in the next hour=3*4=12

Expected number to arrive in an 8 hour day=12*8=96