Continuous Random Variables and their Probability Distributions. See attached file for full problem description.

Continuous Random Variables and their Probability Distributions

If a point is randomly located in an interval (a,b) and if Y denotes the

location of the point, then Y is assumed to have a uniform distribution

over (a,b). A plant efficiency expert randomly selects a location along

a 500 foot assembly line from which to observe the work habits of the

workers on the line. What is the probability that the point she

selects:

a) is within 25 feet of the end of the line

b) is within 25 feet of the beginning of the line

c) is closer to the beginning of the line than to the end of the line.