Question

A company produces optical-fiber cable with a mean of 0.3 flaws per 100 feet. What is the probability that there will be exactly 5 flaws in 1000 feet of cable? Round your answer to four decimal places.

Answer 1

Step 1

Given; A company produces optical-fiber cable with a mean of 0.3 flaws per 100 feet. What is the probability that there will be exactly 5 flaws in 1000 feet of cable? Round your answer to four decimal places.

Step 2

Let X denote the number of flaws in the optical cable.

The mean number of flaws per 100 feet =0.3

Thus the mean number of flaws per 1000 feet is;

`\lambda=0.3*(1000)/(100)=0.3*10=3`
`_^(X\approx P(3))`

Applying the formula

`P(X=x)=(e^(-\lambda)(\lambda)^x)/(x!)`
`\begin{gathered} P(X=x)=(e^(-3)(3)^5)/(5!) \\ x=5 \\ P(X=5)=0.1008 \end{gathered}`

Answer;