# A salesperson goes door-to-door in a residential area to demonstrate the use of

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 $$\displaystyle{90}\%$$ 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 $$\displaystyle{90}\%$$ 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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dieseisB

Step 1
Independent repeated trials of an experiment with two outcomes only are called Bernoulli trials. Call one of the outcomes "success" and the other outcome "failure". Let p be the probability of success in a Bernoulli trial. Then the probability of failure q is given by
$$\displaystyle{q}={1}-{p}$$
$$P(k)=\left(\begin{array}{c}n\\ k\end{array}\right) p^{k} q^{n-k}$$
Step 2
by calculating the probability of giving
$$\displaystyle{p}{\left({0}\right)}+{p}{\left({1}\right)}+{P}{\left({2}\right)}+{p}{\left({3}\right)}+{p}{\left({4}\right)}={.7651}$$