Question

What are the mean and standard deviation of a binomial probability distribution with `n=210` and `p=12/21`?

Answer 1

Mean is `120` and Standard Deviation is `7.171`

Explanation:

Binomial distribution is a frequency distribution of possible number of successful outcomes in given number of trials `n`, in each of which there is the probability of success is `p` (and `q=1-p` is probability of failure).

The mean and standard deviation of a binomial distribution are given by `np` and `sqrt(npq)`.

Here `n=210`, `p=12/21` and `q=1-12/21=9/21`.

Hence Mean is `210xx12/21=120`

Standard Deviation is `sqrt(210xx12/21xx9/21)`

= `1/21xxsqrt22680=150.6/21=7.171`