Question Bank • QB_EXP_EM_005 NAT • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Mean, median, mode and standard deviation

Question Statement:

In a seed germination trial, the number of defects follows a Poisson distribution with mean $\lambda = 2.0$. The probability of observing at least one defect is ________ (rounded off to 2 decimal places).

Answer Key:

0.86

Step-by-Step Solution & Explanation

1. For a Poisson distribution, $P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}$. 2. Probability of at least one defect $P(X \ge 1) = 1 - P(X = 0)$. 3. $P(X = 0) = \frac{e^{-2} \times 2^0}{0!} = e^{-2} \approx 0.135335$. 4. $P(X \ge 1) = 1 - 0.135335 = 0.864665 \approx 0.86$.
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