Topic $8-$ Simulation $-$ Homework

Problem $16-09$

Problem $16-01$

Problem $16-15($Algorithmic$)$

Problem $16-13($Algorithmic$)$

Problem $16-11($Algorithmic$)$

Problem $16-03$

Problem $16-05($Algorithmic$)$

Problem $16-07($Algorithmic$)$

Progress:$1/8$ items

Question Content Area

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Problem $16-09$

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

Player Iowa 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. Use at least $1,000$ trials. What is the average and standard deviation of points scored by the Iowa Energy? If required, round your answer to one decimal place.

Average $=$ fill in the blank $1$

$11\mathrm{.}8$

Standard Deviation $=$ fill in the blank $2$

$4\mathrm{.}9$

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

What is the average and standard deviation of points scored by the Maine Red Claws? If required, round your answer to one decimal place.

Average $=$ fill in the blank $4$

$11\mathrm{.}3$

Standard Deviation $=$ fill in the blank $5$

$3\mathrm{.}1$

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

Let Point Differential $=$ Iowa Energy points $-$ Maine Red Claw points. What is the average point differential between the Iowa Energy and Maine Red Claws? If required, round your answer to one decimal place.

fill in the blank $7$

$0\mathrm{.}5$

What is the standard deviation in the point differential?

fill in the blank $8$

$4\mathrm{.}3$

What is the shape of the point differential distribution?

Left Skewed

What is the probability of that the Iowa Energy scores more points than the Maine Red Claws? If required, round your answer to three decimal places.

fill in the blank $10$

$0\mathrm{.}521$

The coach of the Iowa Energy feels that they are the underdog and is considering a "riskier" game strategy. The effect of the riskier game 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 $1\text{'}$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?

Average $=$ fill in the blank $11$

$13\mathrm{.}2$

Standard Deviation $=$ fill in the blank $12$

$5\mathrm{.}6$

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

The average and standard deviation of the Iowa Energy's point total increased with the risky strategy. The average increased by $1\mathrm{.}4$ points, and the standard deviation increased by $0\mathrm{.}7$ points. The probability of the Iowa Energy scoring more points than the Maine Red Claws also increased to $0\mathrm{.}521.$

How is the probability of the Iowa Energy scoring more points that the Maine Red Claws affected? If required, round your answer to three decimal places.

Probability $=$ fill in the blank $14$

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.