Question

What is the variance and standard deviation for the following problem?

Answer 1

We can find the variance of a binomial experiment as

`\sigma^2=npq`

Using the relation

`p+q=1\Rightarrow q=1-p`

Therefore the variance is

`\sigma^2=np(1-p)`

We have the values of n and p, then

`\begin{gathered} \sigma^2=np(1-p) \\ \sigma^2=10\cdot0.3\cdot(1-0.3) \\ \sigma^2=10\cdot0.3\cdot0.7 \\ \sigma^2=2.1 \end{gathered}`

And we know that the standard deviation is

`\begin{gathered} \sigma^{}=\sqrt[]{np(1-p)} \\ \sigma^{}=\sqrt[]{2.1} \\ \sigma^{}=1.449 \end{gathered}`

Therefore the final answer is

`\begin{gathered} \sigma^2=2.1 \\ \\ \sigma^{}=1.449 \end{gathered}`