Determine the binomial distribution for which the mean is 20 and … - Vidyadip

Question

Determine the binomial distribution for which the mean is $20$ and variance $16$.

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Answer

$n. p = 20, n p q = 16$
$\Rightarrow\text{q}=\frac{16}{20}=\frac{4}{5}\text{ }\text{ }\therefore\text{ }\text{ }\text{p}=\frac{1}{5}\text{and n}=100$
OR The Distribution is P(r) = $100_{\text{C}_\text{r}}\Bigg[\frac{4}{5}\Bigg]^\text{100 - r}\cdot\Bigg(\frac{1}{5}\Bigg)^\text{r},\text{ r = 0,1,2,.....,100.}$

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