Team X Is Scheduled to Play Against Team Y in an Upcoming

Essay

Team X is scheduled to play against Team Y in an upcoming game in Baseball's World Series. Assume that each player's point production can be represented as an integer uniform variable with the ranges provided in the following table:
​ $$\begin{array} { | c | c | c | } \hline \text { Player } & \text { Team X } & \text { Team Y } \\\hline 1 & { [ 4,10 ] } & { [ 2,4 ] } \\\hline 2 & { [ 2,6 ] } & { [ 14,30 ] } \\\hline 3 & { [ 7,20 ] } & { [ 2,20 ] } \\\hline 4 & { [ 3,5 ] } & { [ 1,10 ] } \\\hline 5 & { [ 6,20 ] } & { [ 8,20 ] } \\\hline 6 & { [ 5,10 ] } & { [ 7,12 ] } \\\hline 7 & { [ 7,10 ] } & { [ 14,20 ] } \\\hline 8 & { [ 12,40 ] } & { [ 3,5 ] } \\\hline 9 & { [ 9,20 ] } & { [ 14,25 ] } \\\hline\end{array}$$ ​
a. Develop a spreadsheet model that simulates the points scored by each team.
b. What are the average and standard deviation of points scored by Team X? What is the shape of the distribution of points scored by Team X?
c. What are the average and standard deviation of points scored by Team Y? What is the shape of the distribution of points scored by Team Y?
d. Let Point Differential = Team X points - Team Y points. What is the average point differential between the two teams? What is the standard deviation in the point differential? What is the shape of the point differential distribution?
e. What is the probability that the Team X scores more points than the Team Y?