In a binomial experiment with n=18 and p=0.30, the probability of getting exactly 9 successes is approximately 3.86%.
f(x) is the probability function of the binomial distribution with parameters n and p. It gives the probability of getting exactly x successes in n independent Bernoulli trials with probability of success p.
Given n = 18 and p = 0.30, we want to compute f(9), which is the probability of getting exactly 9 successes in 18 trials. We can use the binomial probability formula to calculate this directly:
f(x) = (nCx) * p^x * (1-p)^(n-x)
Plugging in n = 18, p = 0.30, and x = 9, we get:
f(9) = (18C9) * 0.30^9 * (1-0.30)^(18-9)
f(9) ≈ 0.0386
Therefore, the probability of getting exactly 9 successes in 18 trials is approximately 0.0386 or 3.86%.