Question

a hotel claims that 95% of its customers are very satisfied with its service. there is a sample size of seven customers. A. what is the probability that exactly six customers are very satisfied?B what is the probability that more than six customers are very satisfied?C. what is the probability that less than five customers are very satisfied?D. suppose that of seven customer selected, three responded that they are very satisfied. what conclusions can be drawn about the sample? the probability that three out of seven customers are very satisfied is__, assuming that 95% of customers are very satisfied. therefore, it is__that randomly selecting seven customers would result in three responding that they were very satisfied.(round all answers to four decimal places please)

Answer 1

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:

`P(X=x)=(^n_x)p^x(1-p)^(n-x)_{}`

(a) Probability that exactly 6 customers are satisfied

`\begin{gathered} P(X=6)=(^7_6)(0.95)^6(1-0.95)^(7-6) \\ =\text{ 7}*\text{ 0.7351}*0.05 \\ =\text{ 0.25728} \\ \approx\text{ 0.2573} \end{gathered}`

The probability that exactly six customers are very satisfied is 0.2

(b) Probability that more than 6 customers are very satisfied