Question

Is it possible to have a Binomial distribution with mean 5 and standard

deviation 3. Verify your answer mathematically​

Answer 1

SOLUTION

TO VERIFY

Is it possible to have a Binomial distribution with mean 5 and standard deviation 3

EVALUATION

Let for the given Binomial distribution two parameters are n , p

Then

Mean = np

$\sf{Standard \: Deviation = \sqrt{npq} }$

Now it is given that the Binomial distribution is with mean 5 and standard deviation 3

So by the given condition

$\sf{np = 5 \: \: \: - - - (1)}$

$\sf{ \sqrt{npq} = 3 }$

$\sf{ \implies \: {npq} = 9 }$

$\sf{ \implies \: 5q= 9 }$

$\displaystyle \sf{ \implies \: q= \frac{9}{5} }$

$\displaystyle \sf{ \implies \: 1 - p= \frac{9}{5} }$

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

Which is absurd as probability of an event can not be negative ( 0 ≤ p ≤ 1 )

Hence such Binomial distribution is not possible

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