Question

the brand name of a certain chain of coffee shops has a 53% 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 town. he selects a random sample of 10 coffleton residents. find the probability that the number that recognize the brand name is not 4.

Answer 1

This problem can be solve using the Binomial Distribution, it is a recurrence conveyance of the conceivable number of effective results in a given number of trials in each of which there is a similar likelihood of accomplishment.

Let be X: coffleton residents recognize the brand name 

n = 10 

p = 0.53

q = 0.47 

P(X = 4) = 

(10)
 
(4)*(0.53^4)*(0.47^6) = 0.00340

Answer 2

Using the binomial distribution, it is found that there is a 0.8214 = 82.14% probability that the number that recognize the brand name is not 4.

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:

• The brand name of a certain chain of coffee shops has a 53% recognition rate in the town of coffleton, hence p = 0.53.

• There is a sample of 10 residents, hence n = 10.

The probability that the number that recognize the brand name is not 4 is given by:

$P(X \neq 4) = 1 - P(X = 4)$

In which:

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

$P(X = 4) = C_{10,4}.(0.53)^{4}.(0.47)^{6} = 0.1786$

Then:

$P(X \neq 4) = 1 - 0.1786 = 0.8214$

0.8214 = 82.14% probability that the number that recognize the brand name is not 4.

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