Question

19. 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:                                                                                                    (8)

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Player	Team X	Team Y
1	[4,10]	[2,4]
2	[2,6]	[14,30]
3	[7,20]	[2,20]
4	[3,5]	[1,10]
5	[6,20]	[8,20]
6	[5,10]	[7,12]
7	[7,10]	[14,20]
8	[12,40]	[3,5]
9	[9,20]	[14,25]

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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?

What is the probability that the Team X scores more points than the Team Y?                        

Answer 1

To simulate scores from a uniform distribution [a,b] in excel we will use

=RANDBETWEEN(a,b)

For example =RANDBETWEEN(4,10) will generate uniform random numbers in the interval [4,10]

Prepare the following sheet

Columns A to F

Columns G to K

Columns L to P

The rest

Copy the rows to create 1000 trials

Paste the random numbers as values to avoid changes

Get the following values

We add the following to calculate the average and standard deviations of the points scored by X and Y and the point differentials

Get these values

b) the average and standard deviation of points scored by Team X are 98.45 and 11.22

Plot the distribution using data-->data analysis-->histogram

get the following raw graph

Format as needed

the distribution of points scored by Team X has a bell shape, and symmetrical about mean at around 98

c) the average and standard deviation of points scored by Team Y are 105.75 and 9.55

Get the histogram using

get the following graph

the shape of the points scored by team Y has an approximate bell shape, with a slightly thicker right tail and a mean at around 105

d) the average and standard deviation of point differential between the two teams is -7.30 and 14.45

Get the following histogram

Get the following histogram

The distribution of the point differential has an approximate bell shape, with a left skew (longer left tail). The mean does not coincide with the mode of the distribution

the probability that the Team X scores more points than the Team Y = (count of point differential is greater than 0)/1000

We use the following to get the count and the probability

get these

the probability that the Team X scores more points than the Team Y is 0.294