Question

The brand name of a certain chain of coffee shops has a 52​% recognition rate in the town of Coffleton. 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 8 Coffleton residents. Find the probability that the number that recognize the brand name is not 4. Round to three decimal places.

Answer 1

Answer:

0.728

Step-by-step explanation:

We are given that The brand name of a certain chain of coffee shops has a 52​% recognition rate in the town of Coffleton.

A shopkeeper selects a random sample of 8 Coffleton residents.

Now we are supposed to find the probability that the number that recognize the brand name is not 4.

So, probability of success = p = 0.52

So, q = probability of failure = 1-p = 1- 0.52 = 0.48

n = 8

Now find the probability  the number that recognize the brand name is  4.

Formula : $P(X=r)=^nC_r p^r q ^{n-r}$

$P(X=4)=^8C_4 (0.52)^4 (0.48)^{8-4}$

$P(X=4)=\frac{8!}{4!4!}(0.52)^4 (0.48)^{8-4}$

$P(X=4)=0.271691$

So, $P(x\neq 4)=1 - P(x=4)$

$P(x\neq 4)=1 -0.271691$

$P(x\neq 4)=0.7283$

Hence  the probability that the number that recognize the brand name is not 4 is 0.728