Question

In a binomial distribution, the mean is $4$ and variance is $3$ . Then its mode is :

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (A)

Given, mean $=4$ i.e., $np=4$
and variance $=3$, i.e., $npq=3$
so, $q=3/4$ and $p=1-q=1/4$
and $n=16$
Hence the Binomial distribution is given by
${}^{16}{C}_r{\left(\frac{1}{4}\right)}^r{\left(\frac{3}{4}\right)}^{16-r};r=0,1,\dots \dots .16$
$\therefore$ Mode of the distribution is a number that repeats for the maximum time.
Thus, Mode $=4$.