The sum of of the mean and variance of a binomial distribution is 15 and the sum of their squares is 117. the mean of the distribution is

Options

A. 6
B. 9
C. 3
D. 12

Answer

B

Explanation

Let n and p be parameters of the binomial distribution . Then,
`np+npq=15 and (np)^2+(np)^2+(npq)^2=117" "["Given"]`
`therefore (n^2p^2(1+q^2))/(np+npq)^2=(117)/(15^2)`
`rArr (1+q^2)/((1+q)^2)=(117)/(225)rArr 6q^2-13q+6=0rArr q=(2)/(3) and p=(1)/(3)`
`therefore np+npq=15rArr nxx(1)/(3)+nxx(2)/(9)=15 rArr n=27`