Question

The mean of a binomial distribution is 20, and the standard deviation 4. Find the parameter of the distribution ? With Clean ANswer

Answer 1

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Answer 2

SOLUTION

GIVEN

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

TO DETERMINE

The parameter of the distribution

EVALUATION

Let the parameters are n and p

It is given that mean of a binomial distribution is 20

$\displaystyle \sf{np = 20 \: \: \: - - - (1)}$

Again

$\displaystyle \sf{ \sqrt{npq} = 4\:}$

$\displaystyle \sf{ \implies \:npq = 16\:} \: \: - - - (2)$

From Equation 1 and Equation 2 we get

$\displaystyle \sf{ \implies q = \frac{16}{20} }$

$\displaystyle \sf{ \implies q = \frac{4}{5} }$

$\displaystyle \sf{ \implies 1 - p = \frac{4}{5} }$

$\displaystyle \sf{ \implies \: p = 1 - \frac{4}{5} }$

$\displaystyle \sf{ \implies \: p = \frac{1}{5} }$

From Equation 1 we get

$\displaystyle \sf{ \implies n = 20 \times 5 = 100}$

FINAL ANSWER

Hence the required parameters are

$\displaystyle \sf{ n = 100 \: \: \: \: and \: \: \: \: p = \frac{1}{5} }$

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