Question

If in a binomial distribution the mean is $20$, standard deviation is $\sqrt{15}$, then $p=$

• A. $\frac{3}{4}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

$\frac{1}{4}$

Mean$=np$
$=20$
$S.D^2=$Variance
$=np(1-p)$
Hence, $15=np(1-p)$
$15=20(1-p)$

$\frac{3}{4}=1-p$
$p=\frac{1}{4}$