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

0.728

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)=(8!)/(4!4!)(0.52)^4 (0.48)^(8-4)`

`P(X=4)=0.271691`

So,
`P(x\\eq 4)=1 - P(x=4)`

`P(x\\eq 4)=1 -0.271691`

`P(x\\eq 4)=0.7283`

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