The time $X$ (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with $A=25$ and $B=35$.

• (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 $\mu$ 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?