# What is the variance of a binomial distribution for which n = 75 and p = 0.20?

Nov 1, 2015

75 x $\left(\frac{1}{5}\right)$ x $\left(\frac{4}{5}\right)$

#### Explanation:

The formula for the variance of a binomial distribution is n x p x q where q = 1 - p. Here n = 75, p = .20 or $\left(\frac{1}{5}\right)$ and q = 0.80 or $\left(\frac{4}{5}\right)$ and hence the answer.

Nov 1, 2015

The answer is $12$.

#### Explanation:

Note that if X~ "Bin ( n , p )" then Variance of $X$ is $n p \left(1 - p\right)$.

Now your $n = 75$ and $p = 0.20$.

So your variance = $75 \times 0.20 \times \left(1 - 0.20\right) = 75 \times 0.20 \times 0.80 = 12$