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 10.85 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.

Question

What is the probability that a single pipe will be between 10.07 feet and 10.39 feet long?

Answer 1

You need a double integral.
integral from 10 to 10.85
integral from 10.07 to 10.39 ( only one changed because it is asking for a single pipe.)
integrate the function 1/(10.85-10)^2