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:
\(P(X
eq 4) = 1 - P(X = 4)\)
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:
\(P(X
eq 4) = 1 - 0.1786 = 0.8214\)
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
