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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi
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The distance between flaws on a long cable is

Chapter 4, Problem 4E

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QUESTION:

The distance between flaws on a long cable is exponentially distributed with mean 12 m.

a. Find the probability that the distance between two flaws is greater than 15 m.

b. Find the probability that the distance between two flaws is between 8 and 20 m.

c. Find the median distance.

d. Find the standard deviation of the distances.

e. Find the 65th percentile of the distances.

Questions & Answers

QUESTION:

The distance between flaws on a long cable is exponentially distributed with mean 12 m.

a. Find the probability that the distance between two flaws is greater than 15 m.

b. Find the probability that the distance between two flaws is between 8 and 20 m.

c. Find the median distance.

d. Find the standard deviation of the distances.

e. Find the 65th percentile of the distances.

ANSWER:

Solution

Step 1 of 6

In a long cable the distance between flaws is exponentially distributed with mean 12 m

The mean of exponential distribution is=12

                                                         Then =0.0833

The pmf of Exponential distribution is

The CDF of exponential distribution is

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