Assume there is a rope with the length of 10 feet, Alexa will cut it anywhere along the rope's length with equal probability. Let X be the distance from the starting point to the cutting point.
a) What is the distribution and parameter of X?
b) What is the standard deviation of X?
c) What is the probability that Alexa cut at exactly 6 feet from the starting point?
d) Given that Alexa decided to cut less than 6 feet from the start of the rope, what's the probability she cut less than 3.5 feet from the start?
e) Alexa needs a rope more than 100 inches long, what is the probability she will get such a piece if she makes one random cut along the length of the rope?