Question

A company produces optical-fiber cable with a mean of 0.4 flaws per 100 feet. What is the probability that there will be exactly 5 flaws in 1200 feet of cable? Round your answer to four decimal places.

Answer 1

lambda (λ) is the mean number of events within a given interval of time or space.

`\begin{gathered} \lambda=0.4((1200)/(100)) \\ \\ \lambda=4.8 \end{gathered}`

Also, given;

`x=5`

Thus, the probability is;

`P(X=x)=e^(-\lambda)\cdot(\lambda^x)/(x!)`

Then;

`\begin{gathered} P(5)=e^(-4.8)((4.8^5)/(5!)) \\ \\ P(5)\approx0.1747 \end{gathered}`

ANSWER: 0.1747