In an ordinary 8-hour day, Roto-Drains receives calls for emergency service at an average rate of 1 per hour (otherwise, the calls appear to be random and independent).The owner currently has a crew of technicians capable of handling up to (and including) nine emergencies per day.What is the probability that on a random day there are more calls than her crew can handle?
A).2833
B).2617
C).3419
D).2509
E).2864

Question

Quizplus · Accepted Answer

The probability of receiving more than 9 calls in an 8-hour day is the same as the probability of receiving 10 or more calls in an 8-hour day. The probability of receiving 10 or more calls in an 8-hour day is given by the Poisson distribution with λ = 8:P(X ≥ 10) = 1 - P(X ≤ 9) = 1 - 0.2833 = 0.7167Therefore, the probability that on a random day there are more calls than her crew can handle is 0.7167, or 71.67%.

In an Ordinary 8-Hour Day, Roto-Drains Receives Calls for Emergency