Question

The number of requests for assistance received by a towing service is a Poisson process with rate α = 10 per hour.

(a) Compute the probability that exactly fifteen requests are received during a particular 2-hour period. (Round your answer to three decimal places.)

(b) If the operators of the towing service take a 30 min break for lunch, what is the probability that they do not miss any calls for assistance? (Round your answer to three decimal places.)

(c) How many calls would you expect during their break?

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

a)

Let X denote the number of calls received during a 2 hour period. Then

Required probability =

b)

Let X denote the number of calls received during a 30 minute period. Then

Required probability =

c)

Let X denote the number of calls received during a 30 minute period. Then

So, Number of calls expected during the break =