A salesperson goes door-to-door in a residential area to demonstrate the use of a new household appliance to potential customers. At the end of a demonstration,the probability that the potential customer would place an order for the product is aconstant 0.2107. To perform satisfactorily on the job, the salesperson needs at leastfour orders. Assume that each demonstration is a Bernoulli trial.
a. If the salesperson wants to be at least confident of getting at least
4 orders, at least how many demonstrations should she make?
b. The salesperson has time to make only 22 demonstrations, and she still
wants to be at least confident of getting at least 4 orders. She intends
to gain this confidence by improving the quality of her demonstration and
thereby improving the chances of getting an order at the end of a demonstration. At least to what value should this probability be increased in order to gain the desired confidence? Your answer should be accurate to four decimal places.