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.
P(X=16)
, n=17
, p=0.6
To find P(X=16), we use the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Plugging in the values:
P(X=16) = (17 choose 16) * 0.6^16 * (1-0.6)^(17-16)
P(X=16) = (17 choose 16) * 0.6^16 * 0.4^1
Calculating (17 choose 16):
(17 choose 16) = 17! / (16!(17-16)!)
(17 choose 16) = 17
Plugging in the values:
P(X=16) = 17 * 0.6^16 * 0.4
P(X=16) = 17 * 0.6^16 * 0.4
Calculating:
P(X=16) ≈ 0.0310
Therefore, P(X=16) is approximately 0.0310 when n=17 and p=0.6.