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

Solution:

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

$\begin{gathered} \lambda=0.4(\frac{1200}{100}) \\ \\ \lambda=4.8 \end{gathered}$

Also, given;

$x=5$

Thus, the probability is;

$P(X=x)=e^{-\lambda}\cdot\frac{\lambda^x}{x!}$

Then;

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

ANSWER: 0.1747