Set #1 Instructions: You may work with up to 3 other of your classmates on this project. All calculations should be shown by hand or in Excel or Word. So show your work. Due on September 18th, 11:59 pm. 50 points. 1. You are saving money for 3 years before you build a house. You have two investment options available to help you save. The first option, Plan A, produces a return of 8% a year, with a standard deviation of 1%. The second option, Plan B, also produces a return of 8% a year, but the standard deviation is 4%. Which plan do you choose? Why? [5 points] 2. You are given the following two series on income and credit scores. Inco me 39 27 57 31 34 50 38 62 43 49 FICO 625 600 710 595 610 840 726 710 635 560 (A) Find the covariance and the correlation coefficient. (B) Do credit scores increase, decrease, stay the same, with Income? (C) Create a scatter plot with Income and credit score. What do you see? [10 points] 3. Suppose you flip a fair coin four time. (A) What is the probability you will get all four heads? (B) All four tails? (C) Either all four heads or four tails? (D) Anything but four heads or four tails? [5 points] 4. Crime and Punishment: In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty. (A) If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison. (B) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison. [20 points] 5. In the BS Lottery (which stands for \"Business Statistics\