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?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 least4 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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