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Question
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
Solution
\[\text{ Standard deviation of the binomial distribution} = 4 \]
\[\text{ Variance } = \left( \text{ Standard deviation }\right)^2 \]
\[\text{ Variance, i.e. npq }= 16 \]
\[\text{ Mean } = np = 20\]
\[ \Rightarrow q = \frac{16}{20} = \frac{4}{5}\]
\[\text{ and } p = 1 - q = \frac{1}{5}\]
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