Question

The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 7% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 7% of his customers buy a magazine is correct, what is the probability that exactly 4 out of the first 14 customers buy a magazine

Answer 1

Using the binomial distribution, it is found that there is a 0.0116 = 1.16% probability that exactly 4 out of the first 14 customers buy a magazine.

What is the binomial distribution formula?

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

In this problem:

• 7% of his customers buy a magazine, hence p = 0.07.

• A sample of 14 customers is taken, hence n = 14.

The probability that exactly 4 out of the first 14 customers buy a magazine is P(X = 4), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{14,4}.(0.07)^{4}.(0.93)^{10} = 0.0116$

0.0116 = 1.16% probability that exactly 4 out of the first 14 customers buy a magazine.

More can be learned about the binomial distribution at brainly.com/question/24863377