CA Foundation · Quantitative Aptitude · Theoretical Distributions
A binomial distribution has n = 100 and p = 0.02. Which Poisson distribution gives the best approximation to it?
The best approximation is a Poisson distribution with mean 2, because for large n and small p the binomial is approximated by a Poisson whose mean equals np, which is 100 times 0.02, giving 2. Using npq or q would be incorrect.
- APoisson with mean 2Correct
- BPoisson with mean 0.02
- CPoisson with mean 98
- DPoisson with mean 1.96
Explanation
When n is large and p is small, the binomial is approximated by a Poisson with mean m = np = 100 × 0.02 = 2. Mean 1.96 wrongly uses npq, which is the binomial variance. Mean 0.02 uses p alone, and 98 uses nq.
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