Question: A toll-free phone number is available from 9 a.m. to 9 p.m. for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 0.4 calls are received per minute.

a. What properties must be true about the situation described here in order to use the Poisson distribution to calculate probabilities concerning the number of phone calls received in a 1-minute period? Assuming that this situation matches the properties discussed in (a), what is the probability that during a 1-minute period

b. zero phone calls will be received?

c. three or more phone calls will be received?

d. What is the maximum number of phone calls that will be received in a 1-minute period 99.99% of the time?