Discrete Random Variables

ignment: (17 points total) In an attempt to raise money, an elementary school PTA created a dice game as part of an annual fundraising event. The player will roll a fair die. If they roll a one, they will win $20, and if they roll a two, they will win $5. The PTA will charge $5 to play the game. (5 pts) a Create a valid probability table for the amount the PTA will earn. b) What is the expected value for the PTA of any one game played? Use the binompdf or the binomodf command in your calculator to answer the following questions. To receive credit, you must show the command you used and the values you entered. \\(12 pts) A college student has a part-time job checking newly manufactured hard-drive disks for dents, nicks and scratches. In a case of disks, the probability that they will observe a scratch is 289%. If the student inspects 10 cases: a) What is the probability that they observe 4 scratches? b) What is the probability that they will observe at most 4 scratches? c) What is the probability that they will observe at least 4 scratches? d) What is the probability that they will observe between 2 and 4 scratches (inclusive)? e) What is the mean and standard deviation of the number of scratches observed