At random variable `X~B(n,p)` if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are

Options

A. 54
B. 55
C. 12
D. 18

Answer

B

Explanation

Given, mean =18 and variance=12
`thereforenp=18 and npq=12`
`implies(npq)/(np)=(12)/(18)impliesq=(2)/(3)`
Now, `p=1-q=1-(2)/(3)=(1)/(3)`
On substituting `p=(1)/(3)` in np=8, we get
`n((1)/(3))=18 impliesn=54`
`therefore` value so X are 0,1,2 . .. 54
Hence, total number of possible values of X=55