Answer to Question #263965 in Statistics and Probability for Jazzy

Question

A plastic manufacturing company reports that a particular defect occurs randomly 

in lengths of plastic film produced by a stable manufacturing process at a rate of 3 

defects per 70 metre length. Assume that the length between successive defects 

follows an Exponential distribution. A random section of the plastic film, 35 metres 

in length, was selected and inspected for defects. What is the probability that at 

least 2 defects will be found in the sample? 

Answer 1

$$\lambda=\dfrac{1}{3}\cdot\dfrac{35}{70}=\dfrac{1}{6}$$

$$P(X\geq2)=e^{-{1 \over 6}(2)}\approx0.716531$$

The probability that at least 2 defects will be found in the sample is $0.716531.$