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 : [tex]P(X=r)=^nC_r p^r q ^{n-r}[/tex]
[tex]P(X=4)=^8C_4 (0.52)^4 (0.48)^{8-4}[/tex]
[tex]P(X=4)=\frac{8!}{4!4!}(0.52)^4 (0.48)^{8-4}[/tex]
[tex]P(X=4)=0.271691[/tex]
So, [tex]P(x\neq 4)=1 - P(x=4)[/tex]
[tex]P(x\neq 4)=1 -0.271691[/tex]
[tex]P(x\neq 4)=0.7283[/tex]
Hence the probability that the number that recognize the brand name is not 4 is 0.728