Answer to Question #263965 in Statistics and Probability for Jazzy

Question #263965

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? 


1
Expert's answer
2021-11-10T18:32:01-0500
λ=133570=16\lambda=\dfrac{1}{3}\cdot\dfrac{35}{70}=\dfrac{1}{6}

P(X2)=e16(2)0.716531P(X\geq2)=e^{-{1 \over 6}(2)}\approx0.716531

The probability that at least 2 defects will be found in the sample is 0.716531.0.716531.



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