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JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Probability

Let a random variable

X

have a binomial distribution with mean 8 and variance 4. If

P (X \leq 2) = \frac{k}{2 ^{16}}

, then k is equal to:

(A)17
(B)137✓ Correct
(C)1
(D)121

Answer: (B)

Solution

A binomial distribution has mean

n p = 8

and variance

n pq = 4

, so

q = \frac{4}{8} = \frac{1}{2}

, giving

p = \frac{1}{2}

and

n = 16

. Then

P (X \leq 2) = \frac{( 0 16 ) + ( 1 16 ) + ( 2 16 )}{2 ^{16}} = \frac{1 + 16 + 120}{2 ^{16}} = \frac{137}{2 ^{16}}

, so

k = 137

.

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Single correct option

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