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# If the Mean of a Binomial Distribution is 20 and Its Standard Deviation is 4, Find P. - CBSE (Commerce) Class 12 - Mathematics

ConceptBernoulli Trials and Binomial Distribution

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