Could use some help with this question, thanks! If a point is randomly located i

Question

Could use some help with this question, thanks!

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 uniform distribution over (a,b). A plant efficency 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 points 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


Thanks, will rate lifesaver. Please show all work!

Explanation / Answer

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 500-ft assembly line from which to observe the work habits of the workers on the line.
Y is unfiorm 0 to 500.
probability that the point she selects is
a). within 25 feet of the end of the line?
P(475<y<500)=25/500=0.05

b.) within 25 feet of the beginning line?
P(0<y<25) = 25/500=0.05

c.) closer to the beginning of the line than to the end of the line?
P(0<y<25) +P(475<y<500)= 50/500=0.1

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