Question

For a binomial distribution $\overline{x}=4,\sigma =\sqrt{3}$. Then P(X =r) =

• A. ${}^{16}{C}_r\left(\frac{1}{4}{)}^r\right(\frac{3}{4}{)}^{16-r}$
  
• B. ${}^{12}{C}_r\left(\frac{1}{4}{)}^r\right(\frac{3}{4}{)}^{12-r}$
  
• C. ${}^{16}{C}_r\left(\frac{3}{4}{)}^r\right(\frac{1}{4}{)}^{16-r}$
  
• D. ${}^{12}{C}_r\left(\frac{3}{4}{)}^r\right(\frac{1}{4}{)}^{12-r}$

Answer 1

The correct option is A ${}^{16}{C}_r\left(\frac{1}{4}{)}^r\right(\frac{3}{4}{)}^{16-r}$


np=4
npq=3
$\Rightarrow q=\frac{3}{4},p=\frac{1}{4},n=16$