Question

A hotel claims that 8585​% of its customers are very satisfied with its service. complete parts a through d below based on a random sample of sixsix customers.
a. what is the probability that exactly fivefive customers are very​ satisfied?

Answer 1

We can solve this problem using the binomial distribution. A binomial distribution can be thought of as a success or failure outcome in an experiment or survey that is repeated multiple times. 
Probability function of binomial distribution has the following form:
$P= \frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}$
p represents the probability of each choice we want. k is the number of choices we want and n is the total number of choices.
In our case p=0.85, k=5 and n=6. 
We can now calculate the answer:
$P= \frac{6!}{5!(6-5)!} 0.85^5(1-0.85)^{6-5}=0.39$
The probability is 39%.
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