The time X (in minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a (continuous) uniform distribution with a = 25 and b = 35. a. Give the pdf of X and draw a graph of it. b. What is the probability the preparation time exceeds 33 minutes? c. What is the probability the preparation time is within 2 minutes of the mean time? d. For any a such that 25 < a < a + 2 < 35, what is the probability that the preparation time is between a and a + 2 minutes? e. Find the 25th percentile of X. f. Obtain an expression for how to obtain any percentile (p) of a (continuous) uniform random variable with parameters a and b.
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