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`
`:. Np = 18` and `npq = 12`
`rArr (npq)/(np) = (12)/(18) rArr q = 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 rArr n = 54`
`:.` Values of X are `0,1,2 ".........." 54`
Hence, total number of possible values of `X = 55`