Assume a binomial probability distribution with n = 40 and p = 0.55. What is the standard deviation?

Dec 26, 2017

$\sigma \approx 3.15$

Explanation:

Let $Y$ be a binomial random variable based on $n$ trials and success probability $p$. Then the standard deviation for a binomial probability distribution is given as

$\sigma = \sqrt{n p q}$

where $q$ is the probability of failure, given by $1 - p$.

We have $n = 40$ and $p = 0.55$, so $q = .45$. Then:

$\sigma = \sqrt{40 \cdot 0.55 \cdot .45}$

$\approx 3.15$