CA Foundation · Quantitative Aptitude · Theoretical Distributions
A Poisson distribution has mean 3. Using e^-3 = 0.0498, what is P(X ≤ 2)?
P(X ≤ 2) is about 0.4232. It is the sum of P(0) = 0.0498, P(1) = 0.1494 and P(2) = 0.2241 for mean 3. The value 0.5768 is the complement, representing three or more events.
- A0.4232Correct
- B0.2240
- C0.1494
- D0.5768
Explanation
P(0) = 0.0498; P(1) = 3 * 0.0498 = 0.1494; P(2) = 9/2 * 0.0498 = 0.2241. Sum = 0.0498 + 0.1494 + 0.2241 = 0.4233, which is approximately 0.4232 as given in the options. 0.5768 is the complement, P(X ≥ 3), the wrong tail.
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