1. Although astonishingly above average academically, always acing any and all assignments, as an athlete Ariel's accomplishments are actually astound- ing, an artful agility arousing awe and amazement among attendees at any athletic arena. Despite her special prowess, school rules stipulate that poor Ariel may play only one varsity sport per semester, so each semester she must choose which sports she wishes to play. This Autumn, Ariel must choose between Football, Rugby, and Softball. As her favorite president, Teddy Roosevelt, was famous for his motto, \"Speak softly and carry a. BIG STICK,\" Ariel has a tender spot in her heart for Softball. Uncertain, however, whether she likes this motto because she likes Teddy, or whether she likes Teddy because she likes carrying a BIG STICK, she decides at least to consider other sports where she is less well-armed. a. If Ariel is equally likely to choose any of the three sports, then what is the probability that she chooses: i. To play Rugby? (5) ii. Not to play Softball? (5) iii. To play either Football or Rugby? (5) b. If Ariel is equally likely to choose Football or Rugby, and twice as likely to choose Softball over either Football or Rugby, then what is the probability that she chooses: i. To play Softball? (5) ii. Not to play Football? (5) iii. To play either Rugby or Softball? (5) c. If Ariel is thrice as likely to play Football as Rugby, and twice as likely to play Softball as Football, then what is the probability that she chooses: i. To play Football? (5) ii. Not to play Rugby? (5) iii. To play either Football or Softball? (5) (45) 2. Bright, bold, beautiful, but bizarrely bashful banker Beatrice brazenly bum bountiful bucks by buying basically busted businesses. Through experience, Beatrice believes that the amount of money one of her clients deposits in any given transaction can be characterized a Normal distribution with mean ,u. = $1500 and standard deviation 0 = 2500. a. How should you interpret a Negative deposit? (5) b. What are the probabilities that Beatrice's next customer deposits: i. $1500$2500? ii. > $3000? iii. Nothing, but withdraws cash? (15) c. For the distribution of Beatrice's customer deposits, what are the: i. 40'\" Percentile? ii. InterQuartile Range? (15) (35)