#### Question

If the mean of a binomial distribution is 20 and its standard deviation is 4, find *p*.

#### Solution

\[\text{ Standard deviation of the binomial distribution} = 4 \]

\[\text{ Variance } = \left( \text{ Standard deviation }\right)^2 \]

\[\text{ Variance, i.e. npq }= 16 \]

\[\text{ Mean } = np = 20\]

\[ \Rightarrow q = \frac{16}{20} = \frac{4}{5}\]

\[\text{ and } p = 1 - q = \frac{1}{5}\]

Is there an error in this question or solution?

Solution If the Mean of a Binomial Distribution is 20 and Its Standard Deviation is 4, Find P. Concept: Bernoulli Trials and Binomial Distribution.