Question

A customer support center for Bell Computer Company (BMC) receives an average of 2.5 phone calls every 5 minutes. Assume that the number of calls received follows Poisson distribution with λ = 2.5 in answering the following questions

1. What is the probability that no calls will arrive during the next five minutes?
2. What is the probability that 5 calls will arrive during the next 5 minutes?
3. What is the probability that at least 3 calls will arrive during the next five minutes?
4. What is the probability that at least 3 calls will arrive during the next 10 minutes?
5. What is the probability that no more than 3 calls will arrive during the next 10 minutes?

Answer 1

a) probability that no calls will arrive during the next five minutes =P(X=0)=e^-2.5*2.5⁰/0! =0.0821

b) probability that 5 calls will arrive during the next 5 minutes =P(X=5)=e^-2.5*2.5⁵/5! =0.0668

c) probability that at least 3 calls will arrive during the next five minutes =P(X>=3)=1-P(X<=2)

=1-(P(X=0)+P(X=1)+P(X=2))=1-(e^-2.5*2.5⁰/0!+e^-2.5*2.5¹/1!+e^-2.5*2.5²/2!)=0.4562

d)

probability that at least 3 calls will arrive during the next 10 minutes

=P(X>=3)=1-P(X<=2)

=1-(P(X=0)+P(X=1)+P(X=2))=1-(e^-5*5⁰/0!+e^-5*5¹/1!+e^-5*5²/2!)=0.8753

e)

probability that no more than 3 calls will arrive during the next 10 minutes =P(X<=3)

=P(X=0)+P(X=1)+P(X=2)+P(X=3)=0.2650