Question

. A hotel’s reservation center receives 180 calls on average from 9:00 AM – 10:00 AM, and the number of calls in that hour can be modeled by a Poisson random variable. (a) (8 pts) Find the probability that more than one call come in the one-minute period 9:26 AM – 9:27 AM. (b) (8 pts) Find the probability that the first call after 9:00 AM actually comes in after 9:02 AM.

Answer 1

a)

Let X denote the number of calls in a 1-minute period.

Then

Required probability =

b)

Let X denote the number of calls in a 2-minute period.

Then

Required probability = P(first call after 9:00 AM actually comes in after 9:02 AM)

= P(No call during 9:00 AM to 9:02 AM)