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Question
If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.
Options
36
54
18
27
Solution
If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = 54.
Explanation:
Mean = np = 18 ...(i)
Variance = npq = 12 ...(ii)
∴ `(npq)/(np) = 12/18`
∴ q = `2/3`
∴ p = 1 − q
= `1 - 2/3`
= `1/3`
np = 18 ...[From eqn. (i)]
∴ `n(1/3) = 18`
∴ n = 18 × 3
∴ n = 54
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