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Question:

Let a random variable X have a binomial distribution with mean 8 and variance 4. If P(x ≤ 2) = k/216, then k is equal to?

1

17

121

137

Solution:

Correct option is D. 137

np = 8
npq = 4
q = 1/2 → p = 1/2
n = 16
P(x = r) = 16Cr(1/2)16
P(x ≤ 2) = 16C0 + 16C1 + 16C2/16 = 137/216.