Question

Some restaurants have an average of six men per hour, an average of 12 women per hour, and 12 children per hour. What is the probability of at least two customers coming in five minutes, regardless of age or sex? What are the basic assumptions for calculating this probability?

Answer 1

Ans:

We have to assume that 3 types of arrivals are independent.Then using sum of 3 independent Poisson random variables,overall

mean rate=6+12+12=30 per hour

=0.5 per min

For five min period,on average ,there will 5*0.5=2.5 customers

P(x>=2)=1-P(x=0)-P(x=1)

=1-e^-2.5*2.5⁰/0!-e^-2.5*2.5¹/1!

=1-e^-2.5*(1+2.5)

=0.7127