Question

Does any know how to find the variance using n=122 p= 0.64

Answer 1

The formula to find the variance of a binomial distribution given the values n and p is:

`\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \text{ Where} \\ q=1-p \end{gathered}`

In this case, you have:

`\begin{gathered} n=122 \\ p=0.64 \\ q=1-p \\ q=1-0.64 \\ q=0.36 \end{gathered}`

Then

`\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \sigma^2=122\cdot0.64\cdot0.36 \\ \sigma^2=28.11 \\ \text{ Rounding to the nearest tenth} \\ \sigma^2=28.1 \end{gathered}`

Now, the standard deviation is the square root of the variance. So, you have

`\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{28.1} \\ \sigma=5.3 \end{gathered}`

Therefore, the variance and standard deviation of the binomial distribution with the given values n y p are

`\begin{gathered} \sigma^2=28.1\Rightarrow\text{ Variance} \\ \sigma=5.3\Rightarrow\text{ Standard deviation} \end{gathered}`