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

(b) We have
`P(|X-4|)le4)=P(-2 le X-4 le 2)=P(2 le X le 6)`
`=P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)`
`=""^(8)C_(2)((1)/(2))^(8)+""^(8)C_(3)((1)/(2))^(8)+""^(8)C_(4)((1)/(P(|X-4|le4)=P(-2 le X-4 le 2)=P(2 le X le 6)`
`=P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)`
`=""^(8)C_(2)((1)/(2))^(8)+""^(8)C_(3)((1)/(2))^(8)+""^(8)C_(4)((1)/(2))+""^(8)C_(6)((1)/(2))^(8)`
`=(1)/(2^(8))[28+56+70+56+28]`
`=(238)/(2^(8))=(119)/(128)`