Answer to Question #157570 in Statistics and Probability for justice

Question

The quality control manager of Textiles Ltd. wants to know the probability of getting a specific number of holes or blemishes in a large continuous roll of cloth. Textiles Ltd. sells rolls that contain 10 000 linear meters of cloth. Based on past experience, they have determined that on average there are 3 holes or blemishes per roll. Calculate the probability that in the next roll of cloth sold there are 4 holes or blemishes present.

Answer 1

Let a discrete random variable $X$ be the number of holes or blemishes present: $X\sim Po(\lambda)$

$$P(X=x)=\dfrac{e^{-\lambda}\cdot\lambda^x}{x!}$$

Given $\lambda=3$

$$P(X=4)=\dfrac{e^{-3}\cdot 3^4}{4!}\approx0.16803$$

The probability that in the next roll of cloth sold there are 4 holes or blemishes present is 0.16803.