Question

A binomial distribution has a mean of $5$ and variance $4$. The number of trials is

• A. $20$
• B. $16$
• C. $25$
• D. $10$

Answer 1

The correct option is C $25$

Mean $=\mu =np$ = 5; $n$ = number of trials ; $p$ = probability of success ; $q=(1-p)=$ probability of failure
Variance $={\sigma }^2=npq=4$
$4=np(1-p)=5(1-p)$ ;
$p=\frac{1}{5}$
$\mu =np$ = 5
$n=\frac{5}{p}=5\times \frac{5}{1}=25$