Question

The mean and variance of a binomial distribution are 2 and 1 respectively, then the probability of getting exactly three successes in this distribution is ______.

Options

• 0.25

• 0.75

• 0.52

• 0.57

Answer 1

The mean and variance of a binomial distribution are 2 and 1 respectively, then the probability of getting exactly three successes in this distribution is 0.25.

Explanation:

We have, mean = np = 2
and variance = npq = 1

∴ `"npq"/"np" = "q" = 1/2`

∴ p = `1/2` and n = 4

∴ P(X = 3) = `"^4C_3 (1/2)^3 (1/2)` = 0.25