the following questions showing all work. Full credit will not be given to answers without work shown. If you use Minitab Express include the appropriate output (copy + paste) along with an explanation. Output without explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board. 1. [40 points] The table below displays data concerning Penn State undergraduate and graduate enrollment by campus in Fall 2015. Assume that the population of interest is all 97.494 Penn State students, unless otherwise specified. Use the following notation: U = Undergraduate W = World Campus Data from http://budget.psu.edu/factbook/StudentDynamic/UGGREnrollSummaryByAdvisor.aspx?YearCode=2015Enr&FBPlusIndc=N A. Compute P(U) Answer: Undergraduates = 83436/97494 B. Compute P(W) Answer: World Campus Students =7242/97494 C. Compute P(UC) D. Compute P (U W) E. Compute P (U W) F. If you were to randomly select one Penn State student from this population, what is the probability that the student is a University Park undergraduate student? G. Given that a randomly selected student is an undergraduate student, what is the probability that they are a World Campus student? H. Given that a randomly selected student is not an undergraduate student, what is the probability that they are a World Campus student? I. Using the formulas from the online notes, check if the events U and W are independent. J. Are U and W disjoint events? Why or why not? 2. [44 points] Open the dataset Fall16StData.MTW in Minitab Express. Unless otherwise noted, assume that the population of interest all of the students who responded to this survey. A. Make a contingency table for the dog and cat variables. Copy + paste it here. B. Is a contingency table an appropriate way to display data concerning dog and cat ownership? Why or why not? C. Compute P (Dog) D. Compute P (Dog Cat) E. Compute P (Dog Cat) F. Compute P (Cat Dog) G. Compute P (Dog Cat) H. Make a contingency table for the biological sex and alcohol preference variables. Copy + paste it here. I. Given that a randomly selected student is a male, what is the probability that he prefers beer? J. Given that a randomly selected student is a female, what is the probability that she prefers beer? K. Compute P (FemaleC wine). 3. [16 points] At one university, 88% of students speak English, 60% of students speak French, and 50% of students speak both English and French. A. Are speaking English and speaking French independent events? Show the calculations that you used to determine this. B. What is the probability that a randomly selected student speaks either English or French? C. What is the probability that a randomly selected student speaks neither English nor French? d. Given that a student does not speak French, what is the probability that he or she speaks English