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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi
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The distance between consecutive flaws on a roll of sheet

Chapter 4, Problem 10E

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QUESTION:

The distance between consecutive flaws on a roll of sheet aluminum is exponentially distributed with mean distance 3 m. Let X be the distance, in meters, between flaws.

a. What is the mean number of flaws per meter?

b. What is the probability that a 5 m length of aluminum contains exactly two flaws?

Questions & Answers

QUESTION:

The distance between consecutive flaws on a roll of sheet aluminum is exponentially distributed with mean distance 3 m. Let X be the distance, in meters, between flaws.

a. What is the mean number of flaws per meter?

b. What is the probability that a 5 m length of aluminum contains exactly two flaws?

ANSWER:

Solution

Step 1 of 3

The distance between the two the two flaws of aluminium sheet is exponentially distributed with mean 3 m

The mean of exponential distribution is =3

Now

Exponential distribution provides the length between occurrences and poisson distribution provides occurrences between the length

Let X be the distance between the flaws

Here Xexp(3)

Let Y be the no. of flaws in one meter

Then YPoisson(⅓)

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