$($All answers were generated using $1,000$ trials and native Excel functionality.$)$

The Iowa Energy are scheduled to play against the Maine Red Claws in an upcoming game in the National Basketball Association $($NBA$)$ G League. Because a player in the NBA G League is still developing his skills, the number of points he scores in a game can vary substantially. Assume that each player$$s point production can be represented as an integer uniform random variable with the ranges provided in the following table:

Player lowa Energy Maine Red Claws

$1[5,20][7,12]$

$2[7,20][15,20]$

$3[5,10][10,20]$

$4[10,40][15,30]$

$5[6,20][5,10]$

$6[3,10][1,20]$

$7[2,5][1,4]$

$8[2,4][2,4]$

Develop a spreadsheet model that simulates the points scored by each team and the difference in their point totals.

$($a$)$ What are the average and standard deviation of points scored by the Iowa Energy?

Round your answers to one decimal place.

Average:

$84\mathrm{.}5$

Standard Deviation:

$11\mathrm{.}5$

What is the shape of the distribution of points scored by the Iowa Energy?

Uniform

$($b$)$ What are the average and standard deviation of points scored by the Maine Red Claws?

Round your answers to one decimal place.

Average:

Standard Deviation:

What is the shape of the distribution of points scored by the Maine Red Claws?

$-$ Select your answer $-$

$($c$)$ Let Point Differential $=$ Iowa Energy points $$ Maine Red Claw points. What is the average Point Differential between the Iowa Energy and Maine Red Claws? What is the standard deviation of the Point Differential? If your answer is negative, enter a minus sign in the input box.

Round your answers to one decimal place.

Average:

Standard Deviation:

What is the shape of the Point Differential distribution?

$-$ Select your answer $-$

$($d$)$ What is the probability that the Iowa Energy scores more points than the Maine Red Claws?

Round your answer to the nearest whole number.

$\%$

$($e$)$ The coach of the Iowa Energy feels that they are the underdog and is considering a riskier game strategy. The effect of this strategy is that the range of each Energy player$$s point production increases symmetrically so that the new range is $[0,$ original upper bound $+$ original lower bound$].$ For example, Energy player $1$s range with the risky strategy is $[0,25].$ How does the new strategy affect the average and standard deviation of the Energy point total? How does that affect the probability of the Iowa Energy scoring more points than the Maine Red Claws?

Round first two numerical answers to one decimal place and the last answer to a whole percentage.

The average Iowa Energy point total is relatively unchanged at

points, and the standard deviation of the Iowa Energy point total

$-$ Select your answer $-$

points. The probability of the Iowa Energy scoring more points than the Maine Red Claws

$-$ Select your answer $-$

$\%.$