Let X be the number of customers satisfied
Given:
Sample size (n) = 7
The probability that a customer is very satisfied = 0.95
The probability distribution function for a binomial distribution is:
[tex]P(X=x)=(^n_x)p^x(1-p)^{n-x}_{}[/tex](a) Probability that exactly 6 customers are satisfied
[tex]\begin{gathered} P(X=6)=(^7_6)(0.95)^6(1-0.95)^{7-6} \\ =\text{ 7}\times\text{ 0.7351}\times0.05 \\ =\text{ 0.25728} \\ \approx\text{ 0.2573} \end{gathered}[/tex]The probability that exactly six customers are very satisfied is 0.2
(b) Probability that more than 6 customers are very satisfied
