In eight throws of a die 5 or 6 is considered a success, find the mean number of successes and the standard deviation.

Explanation

Let `X` denote the number of successes in `8` throws.

`n=8`

`p=` probability of getting `5 or 6=
frac{2}{6}=frac{1}{3} and q=frac{2}{3}`

Mean `(n p)=frac{8}{3}`

Variance `(n p q)=frac{16}{9}`

Standard deviation `=sqrt{text { Variance }}=frac{4}{3}`

So, mean` =2.66 ` and standard deviation `=1.33`