Financial Risk Manager Part 1

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Explanation:

The first step is to estimate the number of expected defects in 1,000 runs as follows: (1,000)(0.005) = 5. Next, the mathematical formula for the Poisson distribution for estimating 7 defects given that 5 are expected is:

P(X = 7) = \frac{5^7 e^{-5}}{7!} = \frac{78,125 \times 0.006738}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} = 0.104

(Book 2, Module 14.1, LO 14.a)

Explanation:

P(X = 7) = \frac{5^7 e^{-5}}{7!} = \frac{78,125 \times 0.006738}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} = 0.104

(Book 2, Module 14.1, LO 14.a)

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Question 62

Firm B uses a proprietary forecasting model that requires parameter estimates of random variables that are believed to follow the Poisson distribution. An analyst at Firm B is attempting to assess the probability of the number of defects in an assembly production process for a given company. Assume that there is a 0.005 probability of a defect for every production run. What is the probability of 7 defects in 1,000 production runs?

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Last updated: June 29, 2026 at 12:47

3.0%.

4.4%.

8.6%.

10.4%.