A salesperson goes door-to-door in a residential area to demonstrate the use ofa new household appliance to the potential customers. At the end of ademonstration, the probability that the potential customer would place an orderfor the product is a constant 0.2107. To perform satisfactorily on the job, thesalesperson needs at least 4 orders. Assume that each demonstration is aBernoulli trial.

a) If the salesperson makes 15 demonstrations, what is the probability thatthere would be exactly 4 orders?

b) If the salesperson makes 16 demonstrations, what is the probability thatthere would be at most 4 orders?

c) If the salesperson makes 17 demonstrations, what is the probability thatthere would be at least 4 orders?

d) If the salesperson makes 18 demonstrations, what is the probability thatthere would be anywhere from 4 to 8 (both inclusive) orders?

e) If the salesperson wants to be at least 90% confident of getting at least 4orders, at least how many demonstration should he/she make? (HINT:think about 90% as probability of getting at least 4 orders)