If the mean of a binomial distribution is 12 and its standard deviation is 2, then the number of trials is :
Answer & explanation
Correct answer: option 1
$X \sim B(n,p)$
Mean $=np=12$
Standard deviation $=\sqrt{npq}=2$
$npq=4$
Using $np=12$:
$12q=4$
$q=\frac{1}{3}$
$p=1-q=\frac{2}{3}$
$np=12$
$n\cdot\frac{2}{3}=12$
$n=18$
The number of trials is $18$.