The mean of a binomial distribution is 20, and the standard deviation 4. Calculate parameters of the binomial distribution.

Explanation

Given that mean, i.e. `n p=20`

and standard deviation, i.e. `n p q=4`

`sqrt{n p q}=4 `

`Rightarrow n p q=16 ldots(2)`

Dividing ` eq (2)` by `eq (1)`, we get

`q=frac{16}{20}=frac{4}{5}`

`and p=frac{1}{5};`

`therefore n=frac{text { Mean }}{p}=100 `

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