CA Foundation · Quantitative Aptitude · Theoretical Distributions
A binomial variate has parameters n = 10 and p = 0.5. Which statement about its distribution is correct?
The distribution is symmetric. When p equals 0.5, the probabilities of k successes and n−k successes are equal, so the shape is symmetric about the mean of 5, and skewness is zero. Variance of 2.5 is below the mean.
- AIt is positively skewed
- BIt is negatively skewed
- CIt is symmetricCorrect
- DIts variance is greater than its mean
Explanation
When p = 0.5 the binomial distribution is symmetric about n/2 = 5. Skewness is (q − p)/√npq = 0. Variance = 2.5 which is less than the mean of 5, so the last option is false.
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