A manufacturer has designed a process to produce pipes that are 10 feet long. Th

Question

A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process.

What is the probability that the second pipe (with length Y) is more than 0.38 feet longer than the first pipe (with length X)? Give your answer to four decimal places. Hint: Do not use calculus to get your answer.

Explanation / Answer

The probability distribution of differences (d) in pipe length is triangular, with its peak at d = 0. The proportion of the area that is greater than 0.26 is (1 - (0.38/0.57))^2)/2 = 0.0555

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