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. h)What is the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X)

The probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is 0.2059

Step-by-step explanation:

Let X and Y represent the lengths of two different pipes produced by the process.

Density function of X and Y is :

Expected length of 1 pipe is :

The variance of length of pipe :

To Find the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X)

Hence the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is 0.2059

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