# Question

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.

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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