If the mean and variance of a random variable X having a binomial distribution of 8 terms, are 4 and 2, respectively. Then `P(X gt 6)` is equal to

Options

A. `(1)/(256)`
B. `(3)/(256)`
C. `(9)/(256)`
D. `(7)/(256)`

Answer

C

Explanation

Given, np = 4, npq = 2
`rArr p=q=(1)/(2)`
`therefore n=4xx2=8`
`therefore P(X gt 6)=" "^(8)C_(7)((1)/(2))^(7)((1)/(2))+" "^(8)C_(8)((1)/(2))^(8)`
`=(8)/(256)+(1)/(256)=(9)/(256)`