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If for a Binomial distribution the mean is 10 and the standard deviation is $\sqrt{5}$ then P (x = r) =

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${}^{20}C_{r} {(\frac{1}{2})}^{20}$

${}^{9}C_{r} {(\frac{1}{3})}^{r} {(\frac{2}{3})}^{9 - r}$

${}^{12}C_{r} {(\frac{2}{3})}^{r} {(\frac{1}{3})}^{12 - r}$

$^{12} C_{r} {(\frac{1}{3})}^{r} {(\frac{2}{3})}^{9 - r}$

answer is A.

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Detailed Solution

$p (X = r) = {}^{n}C_{r} . q^{n - r} . p^{r}$

$μ = n p = 10$

$σ^{2} = n p q = 5$

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