If X follows a binomial distribution with parameters n = 8 and $p=\frac{1}{2}$ , then P(| X − 4 |≤ 2) equals

$\frac{119}{128}$

We have,

$P(|X-4|≤2)= P(-2≤X-4≤2)= P(2≤X≤6)=P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)$

$={^8C}_2 \left(\frac{1}{2}\right)^8+={^8C}_3 \left(\frac{1}{2}\right)^8+={^8C}_4 \left(\frac{1}{2}\right)^8+={^8C}_5 \left(\frac{1}{2}\right)^8+={^8C}_6 \left(\frac{1}{2}\right)^8=\frac{1}{2^8}[28+56+70+56+28]=\frac{238}{2^8}=\frac{119}{128}$