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CA Foundation · Quantitative Aptitude · Theoretical Distributions

For a binomial distribution with n = 20 and p = 0.3, what are the mean and the variance respectively?

The mean is 6 and the variance is 4.2. For a binomial distribution the mean equals np, which is 20 times 0.3, and the variance equals npq, which is 20 times 0.3 times 0.7.

  1. AMean 6, variance 4.2Correct
  2. BMean 6, variance 1.8
  3. CMean 4.2, variance 6
  4. DMean 6, variance 14

Explanation

Mean = np = 20 × 0.3 = 6. Variance = npq = 20 × 0.3 × 0.7 = 4.2. Option giving variance 14 uses nq as the variance, which is the mean of failures, not the variance. Option with 1.8 uses npq with wrong q=0.3 and p... (20×0.3×0.3).

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