Question Bank • QB_EM_ADV_073
MCQ • 1 Mark
Section 1: Engineering Mathematics
Probability and Statistics
Subtopic: Poisson, normal and binomial distributions
Question Statement:
For a Binomial distribution $B(n, p)$, the mean is $6$ and the variance is $4$. The number of trials $n$ is:
Options:
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(A) $18$
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(B) $12$
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(C) $24$
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(D) $9$
Step-by-Step Solution & Explanation
For a binomial distribution:
$\mu = n p = 6$
$\sigma^2 = n p q = 4, \quad \text{where } q = 1 - p$
Dividing variance by mean:
$\frac{n p q}{n p} = q = \frac{4}{6} = \frac{2}{3}$
$p = 1 - q = 1 - \frac{2}{3} = \frac{1}{3}$
$n = \frac{6}{p} = \frac{6}{1/3} = 18$
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