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 a constant 0.2107. To perform satisfactorily on the job, the salesperson needs at least four orders. Assume that each demonstration is a Bernoulli trial. a. If the salesperson makes 15 demonstrations, what is the probability that there would be exactly 4 orders? b. If the salesperson makes 16 demonstrations, what is the probability that there would be at most 4 orders? c. If the salesperson makes 17 demonstrations, what is the probability that there would be at least 4 orders?

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Chapter1: Combinatorial Analysis
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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 a
constant 0.2107. To perform satisfactorily on the job, the salesperson needs at least
four orders. Assume that each demonstration is a Bernoulli trial.
a. If the salesperson makes 15 demonstrations, what is the probability that
there would be exactly 4 orders?
b. If the salesperson makes 16 demonstrations, what is the probability that
there would be at most 4 orders?
c. If the salesperson makes 17 demonstrations, what is the probability that
there would be at least 4 orders?
d. If the salesperson makes 18 demonstrations, what is the probability that
there 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
4 orders, at least how many demonstrations should she make?
f. The salesperson has time to make only 22 demonstrations, and she still
wants to be at least 90% 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.

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