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\times\frac{1000}{100}=0.3\times10=3$$_^{X\approx P(3)}$

Applying the formula

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

Answer;