Question Bank • QB_EM_159 NAT • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Poisson, normal and binomial distributions

Question Statement:

The number of tractor breakdowns occurring in a farm fleet follows a Poisson distribution with an average rate of $\lambda = 2$ breakdowns per month. Calculate the probability of observing EXACTLY ZERO breakdowns in a given month (take $e^{-2} = 0.1353$; round off to 3 decimal places).

Answer Key:

0.135

Step-by-Step Solution & Explanation

Poisson probability mass function: $P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}$ For $k = 0$ and $\lambda = 2$: $P(X = 0) = \frac{e^{-2} (2)^0}{0!} = e^{-2} \approx 0.1353 \approx 0.135$
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