CA Foundation · Quantitative Aptitude · Theoretical Distributions
A Poisson distribution is used to approximate a binomial distribution with n = 200 and p = 0.02. What is the mean of the approximating Poisson distribution?
The mean of the approximating Poisson distribution is 4. The Poisson parameter equals np for the binomial, which is 200 multiplied by 0.02, giving 4. The figure 3.92 is the binomial variance npq, not the Poisson mean.
- A4Correct
- B3.92
- C0.4
- D10
Explanation
The Poisson parameter is m = np = 200 × 0.02 = 4. Option B is the binomial variance npq = 3.92, which is not the Poisson mean. Option C wrongly uses n × p/ 10 and option D uses n/p ratio errors.
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