The time X (minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 20 and B = 30.
(a) Write the pdf of X and sketch its graph.
(b) What is the probability that preparation time exceeds 27 minutes?
(c) Find the mean preparation time, then calculate the probability that preparation is within 2 minutes of the mean time?
(d) For any a such that 20 < a < a + 2 < 30, what is the probability that preparation time is between a and a + 2 minutes?