JEE Advanced · MathematicsHard

$A random variable X follows a binomial distribution B (n, p) . If E (X) = 6 and V a r (X) = 4.2, find the value of n .$

A. $10$
B. $20$
C. $30$
D. $15$

Show correct answer & step-by-step solution

Correct answer: B — $20$

Solution

We have n p = 6 and n pq = 4.2 . Dividing these gives q = 4.2/6 = 0.7 . Since p = 1 - q = 0.3, we substitute into n p = 6 to get n (0.3) = 6, which implies n = 20 .

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