Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

Question

P(X=17)
, n=19
, p=0.9

Answer 1

Using the formula for the probability mass function of a binomial distribution:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Plugging in the values n=19, p=0.9, and k=17:

P(X=17) = (19 choose 17) * 0.9^17 * 0.1^2

Calculating (19 choose 17):

(19 choose 17) = 19! / (17!(19-17)!) = 19! / (17!*2!) = 171

Plugging in the calculated values:

P(X=17) = 171 * (0.9)^17 * (0.1)^2

P(X=17) ≈ 0.1166

Therefore, the probability of X=17 when n=19 and p=0.9 is approximately 0.1166.