1. No one likes to wait at a bus stop for very long. A city bus line states that the length of time a bus is late is uniformly distributed between 0 and 10 minutes.

(a) Sketch the distribution for the variable x= time late (in minutes). Be sure to provide all important features such as scales on both axes.

(b) For the distribution in part (a), what proportion of the time will a bus arrive no more than 3 minutes late?

(c) The mean time a bus will be late is 5 minutes according to the distribution in part (a). The director has been receiving a number of complaints from its riders regarding how late buses have been running. He obtains the help of a statistician to test the alternative theory that the mean time a bus will be late is greater than 5 minutes.

1. What is the direction of extreme for this test?
2. Suppose that a randomly selected bus results in the bus arriving 9 minutes late. What is the corresponding p-value for this observation?
3. At = 0.15, what is the decision?