The brand name of a certain chain of coffee shops has a 53% recognition rate in the town of Coffeeton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 7 Coffeeton residents. Find the probability that exactly 4 of the 7 Coffeeton residents recognize the brand name. A) 0.00819B) 287C) 0.0789D) 0.254

B) 0.287

Step-by-step explanation:

For each Coffeeton resident, there are only two possible outcomes. Either they recognize the brand name, or they do not. The probability of a resident recognizing the brand name is independent of other residents. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

53% recognition rate in the town of Coffeeton.

This means that

Find the probability that exactly 4 of the 7 Coffeeton residents recognize the brand name.

This is P(X = 4) when n = 7. So

So the anwer is:

B) 0.287