Question

The mean and a binomial is 40 and standard deviation is 6.. calculate npq.
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Answer 1

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Answer 2

Given,

The mean of the binomial distribution = 40

And the standard deviation = 6

To find,

The values of n, p and q.

Solution,

In the binomial distribution,

Mean = np

Standard deviation = $\sqrt{npq}$

By comparing we get,

$np=40\\\sqrt{npq}=6$ .....(i)

or $npq=36$ .....(ii)

On dividing both the equations i.e. equation (i) and (ii) we have,

$\frac{npq}{np} =\frac{36}{40}\\ q=\frac{9}{10}$

Now, we know that,

$p+q=1\\p=1-q\\p=1-\frac{9}{10} \\p=\frac{1}{10}$

Taking equation (i)

$np=40\\n(\frac{1}{10})=40\\n=400$

Hence, the values of n, p and q are 400, $\frac{1}{10}$ and $\frac{9}{10}$ respectively.