Question

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.

a.Compute the probability of receiving one call in a 10 -minute interval of time.

b.Compute the probability of receiving exactly11 calls in 15 minutes.

c.Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?

What is the probability that none will be waiting?

d. If no calls are currently being processed, what is the probability that the agent can take 2 minutes for a personal time without being interrupted by a call?

Answer 1

Answer 2

here the probability used should be poisson

λ=48

a)

here x=3 λ₁=48*(5/60)=4

b)

x=10λ=48*(15/60)=12

c)

callers to be expected by that time=48*(5/60)

=4

probability that
none will be waiting=1-f(x=0)

λ=4

=1-e^-4

d)

P(x=0)

λ=48*(3/60)

=2.4