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.

Question

Philoid · Accepted Answer

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)= ⁿC_r p^r q^n-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 ]