CA Foundation · Quantitative Aptitude · Theoretical Distributions
Which statement is correct for a binomial distribution with n = 8 and p = 0.5?
The distribution is symmetrical. A binomial distribution is symmetric whenever p = 0.5, regardless of n. Here the mean is 4 and the variance is 2, so the claim about variance being four times the mean is false, and there is no skewness.
- AIt is skewed to the right
- BIt is skewed to the left
- CIt is symmetricalCorrect
- DIts variance is 4 times its mean
Explanation
A binomial distribution is symmetrical when p = 0.5. Here the mean is 4 and variance is 8 × 0.5 × 0.5 = 2, so variance is half the mean, not four times. Skewness arises only when p differs from 0.5.
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