7. The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniformdistribution with A25 and B35.

a. Write the pdf of X and sketch its graph.

b. What is the probability that preparation time exceeds 33 min?

c. What is the probability that preparation time is within 2 min of the mean time? [Hint: Identify m from the graph of f(x).]

d. For any a such that 25  a  a  2  35, what is the probability that preparation time is between a and a  2 min?