To be sure that all math formatting is properly displayed, you are strongly encouraged to reload this page after opening. You should also reload this page if "Math Error" appears in place of math problems. The following problems reflect the reading material you had to prepare for this week. From the list below, choose one problem, write it down, and solve it in detail (show all of your steps). You should pick a problem that has not yet been attempted if you can. Please label your solution with the corresponding question number. In your solutions, you are only to use the math concepts that have been covered in this course up to this point.3. The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is less than 5 minutes. A random sample of 20 waiting times has a mean of 4.2 minutes with a standard deviation of 2.1 minutes. a) The sample mean is 4.2. Before doing any work, what is gut feeling about the chances of the population mean being less than or equal to 5? Do you think that the sample mean of 4.2 is low enough and provides enough evidence? b) Which will you use to perform the hypothesis test, a z-test or t-test? Explain why. c) At = 0.01, test the bus company's claim. Assume the distribution is normally distributed. d) Complete the hypothesis test and compare your results with your guess in part a