Answer:
P(X = 7) = 0.3826
Step-by-step explanation:
We are given that a hotel claims that 90% of its customers are very satisfied with its service. A random sample of eight customers is chosen.
The Binomial probability distribution is given by;
[tex]P(X=r) = \binom{n}{r}p^{r}(1-p)^{n-r} , x = 0,1,2,3,...[/tex]
where, n = number of trials (samples) taken = 8
r = number of success
p = proportion of customers that are satisfied with hotel's service,
i.e.; p = 0.90
Let = Number of customers that are very satisfied
So, Probability that seven customers are very satisfied = P(X = 7)
P(X = 7) = [tex]\binom{8}{7}0.9^{7}(1-0.9)^{8-7}[/tex]
= 8 * [tex]0.9^{7} * 0.1^{1}[/tex] = 0.3826
Therefore, probability that seven customers are very satisfied is 0.3826.
