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Mark the correct alternative in the following:
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X – 4)| ≤ 2) equals.
Given:
n=8
p= 1/2
P (|X – 4)| ≤ 2)=?
Since |X – 4)| ≤ 2
i.e. (x-4) ≤ 2
OR (4-X) ≤ 2
x ≤ 6
OR 2 ≤ x
P (|X – 4)| ≤ 2)= P (2≤x≤ 6)
=p(x=2)+ p(x=3)+ p(x=4)+ p(x=5)+ p(x=6)
P(x=r)= nCr pr qn-r
P (2≤x≤ 6) = 8C2 p2 q6 + 8C3 p3 q5 + 8C4 p4 q4 + 8C5 p5 q3 + 8C6 p6 q2
=p8 [8C2 +8C3 +8C4 + 8C5 + 8C6 ]