Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x = 0) or up to 30 minutes late (x = 30), with all intervals of equal time between x = 0 and x = 30 being equally likely. For example, your friend is just as likely to be from 3 to 4 minutes late as he is to be 25 to 26 minutes late. The random variable X can be any value in the interval from 0 to 30, that is, 0 ≤ x ≤ 30. Because any two intervals of equal length between 0 and 30, inclusive, are equally likely, the random variable X is said to follow a uniform probability distribution.
(a) Find the probability that your friend is between 15 and 25 minutes late.
(b) It is 10 a.m. There is a 90% probability your friend will arrive within the next ______minutes.