If X follows a binomial distribution with parameters `n=8` and `p=1//2`, then `p(|X-4|le2)` equals

Options

A. `(118)/(128)`
B. `(119)/(128)`
C. `(117)/(128)`
D. none of these

Answer

B

Explanation

We have,
`P(|X-4|le2)=P(-2leX-4le 2)=P(2le X le 6)`
`=P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)`
`=.^8C_2((1)/(2))^8=+.^8C_3((1)/(2))^8+.^8C_(4)((1)/(2))^8+.^8C_5((1)/(2))^8+.^8C_6((1)/(2))^8`
`(1)/(2^8){28+56+70+56+28}=(238)/(2^8)=(119)/(128)`