CA Foundation · Quantitative Aptitude · Theoretical Distributions
A binomial distribution has n = 400 and p = 0.01. A Poisson approximation is used with the same mean. What is the variance of the approximating Poisson distribution, and how does it compare with the exact binomial variance?
The Poisson variance is 4, slightly greater than the exact binomial variance of 3.96. The mean is np = 4, and a Poisson variance equals its mean, whereas the binomial variance is npq = 4 × 0.99 = 3.96.
- A4; it is slightly greater than the binomial variance of 3.96Correct
- B4; it is equal to the binomial variance
- C3.96; it is equal to the binomial variance
- D3.96; it is slightly less than the binomial variance of 4
Explanation
Mean = np = 400 × 0.01 = 4. Poisson variance equals its mean, so it is 4. Exact binomial variance = npq = 4 × 0.99 = 3.96. Thus Poisson variance is slightly larger. Options giving 3.96 for Poisson wrongly use npq.
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