If X has a binomial distribution with n = 8 and p = 0.3, then P(X = 4) = ?
To find P(X = 4) when X has a binomial distribution with n = 8 and p = 0.3, we can use the formula for the binomial probability mass function:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Plugging in n = 8, p = 0.3, and k = 4 into the formula:
P(X = 4) = (8 choose 4) * (0.3)^4 * (1-0.3)^(8-4)
Calculating (8 choose 4):
(8 choose 4) = 8! / (4!*(8-4)!) = 70
Plugging in and solving the rest of the formula:
P(X = 4) = 70 * (0.3)^4 * (0.7)^4 = 0.12087368
Therefore, P(X = 4) is approximately 0.1209.