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? Il. Suppose that a randomly selected bus results in the bus arriving 9 minutes late. What is the corresponding p-value for this observation? Ill. At a = 0.15, what is the decision? 2. Suppose that the weight of tomato juice in mechanically filled cans follows a normal distribution with a mean of 464 grams and a standard deviation of 8 grams. The mean of the distribution can be set by adjusting the filling machinery, while the standard deviation reflects the precision of the filling machinery. (a) What proportion of cans contain between 454 and 474 grams of tomato juice? (b) How much tomato juice must a can contain in order for it to be in the top 10% of the distribution of weights? (c) Without performing any calculations, explain how your answer to part (a) will be affected if the standard deviation were halved