Problem 79E

Flaws in plastic-coated wire. The British Columbia Institute of Technology provides on its Web site (www.math.bcit.ca) practical applications of statistics at mechanical engineering firms. The following is a Poisson application. A roll of plastic-coated wire has an average of .8 flaws per 4-meter length of wire. Suppose a quality-control engineer will sample a 4-meter length of wire from a roll of wire 220 meters in length. If no flaws are found in the sample, the engineer will accept the entire roll of wire. What is the probability that the roll will be rejected? What assumption did you make to find this probability?

Answer

Step 1 of 1

The following is a Poisson application.

We have given a roll of plastic-coated wire has an average of of wire.

Suppose an engineer will sample a of wire from a roll of wire in length.

If no flaws are found in the sample, the engineer will accept the entire roll of wire.

We are asked to find the probability that the roll will be rejected and state the assumption you have made to find the probability.

Let be the number of flaws in a of wire.

Since we have given our process has a Poisson distribution and parameter is

Hence we can write,

A random variable is said to have a Poisson probability distribution if and only if

…………(1)

The roll will be rejected if there is at least one flaw in the sample of a of wire.

We need to find

Therefore,

Hence using equation (1), we can write,

Hence the probability that the roll will be rejected is

Since the process has a Poisson distribution, we have assumed that the flaws are randomly distributed and the 4-meter length of sample wire represent the entire roll.