CA Foundation · Quantitative Aptitude · Theoretical Distributions
Two firms record defective items. Firm A's count follows a binomial distribution with n = 20 and p = 0.2. Firm B's count follows a Poisson distribution with mean 4. Which statement is correct?
Both have the same mean of 4, but Firm A's variance is smaller. For Firm A, mean is 20 x 0.2 = 4 and variance is 20 x 0.2 x 0.8 = 3.2. For Firm B, Poisson mean and variance are both 4.
- ABoth have the same mean, but Firm A's variance is smallerCorrect
- BBoth have the same mean and variance
- CFirm A has a larger mean than Firm B
- DBoth have the same variance, but different means
Explanation
Firm A: mean = 20 x 0.2 = 4 and variance = 20 x 0.2 x 0.8 = 3.2. Firm B: mean = 4 and variance = 4. The means are equal, while A's variance 3.2 is smaller than B's 4. So the same-variance options are wrong.
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