Q9) A company installs new central heating furnaces, and has found that for 15% of all installations a return visit is needed to make some modifications. Six installations were made in a particular week. Assume independence of outcomes for these installations.

a. What is the probability that a return visit was needed in all of these cases?

b. What is the probability that a return visit was needed in none of these cases?

c. What is the probability that a return visit was needed in more than one of these cases?

5.45) A toll-free phone number is available from 9 A.M. to 9P.M. for your customers to register complaints about a productpurchased from your company. Past history indicates that an average of 1.5 calls are received per minute.

A.) What properties must be true about the situationdescribed here in order to use the poisson distribution tocalculate probabilities concerning the number of phone callsreceived 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 bereceived in a 1-minute period 99.99% of the time?