Question

Determine the probability p(2) for a binomial experiment with n=12 trials and the success probability p=0.1. Then find the mean, variance, and standard deviation

1. Determine the probability P(2). Round the answer to at least three decimal places.
2. Find the mean. If necessary, round the answer to two decimal places.
3. Find the variance and standard deviation. If necessary, round the variance to two decimal places and standard deviation to at least three decimal places.

Answer 1

Here, n = 12, p = 0.1, (1 - p) = 0.9 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 2)
P(X = 2) = 12C2 * 0.1^2 * 0.9^10
P(X = 2) = 0.230

mean = np
= 12 * 0.1
= 1.20

variance = npq
= 12 * 0.1 * (1-0.1)
= 1.08

std.dev = sqrt(1.08)
= 1.039