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Okay, you guessed it! More Miami Heat data! I know you might be…
Okay, you guessed it! More Miami Heat data! I know you might be getting a little tired of basketball data, and I understand, but stick with it! The reason I’m using the same dataset over and over again is so that you can see how we can use different types of statistical analyses to answer different types of questions. Remember our data on points per game? Let’s revisit those data again. We’re going to use what we know about z-scores to compare players on this team to each other!
PLAYER’S NAME POINTS PER GAME in 21-22 season
Bam Adebayo 19.1
Caleb Martin 9.2
Chris Silva 2.9
Dewayne Dedmon 6.3
Duncan Robinson 10.9
Gabe Vincent 8.7
Haywood Highsmith 2.3
Javonte Smart 5
Jimmy Butler 21.4
KZ Okpala 3.7
Kyle Guy 3.9
Kyle Lowry 13.4
Marcus Garrett 1.1
Markieff Morris 7.6
Max Strus 10.6
Mychal Mulder 7
Nik Stauskas 5.5
Omer Yurtseven 5.3
P.J. Tucker 7.6
Tyler Herro 20.7
Udonis Haslem 2.5
Victor Oladipo 12.4
Flag question: Spacer
Do you remember the mean and standard deviation for points per game from the Miami Heat? Great! You’ll need it for this assignment so you’ll have to go back to previous assignments to get those values (or you can calculate them again if you did not save your answers).
Flag question: Question 1Question 10.5 pts
How many players are below the average?
Group of answer choices
5
6
12
13
Flag question: Question 2Question 20.5 pts
How many players are above the average?
Group of answer choices
12
13
5
9
Flag question: Question 3Question 30.5 pts
Calculate the z score for Jimmy Butler. Round your answer to three decimal places.
Flag question: Question 4Question 40.5 pts
Calculate the z score for Tyler Herro. Round your answer to three decimal places.
Flag question: Question 5Question 50.5 pts
Calculate the z score for Bam Adebayo. Round your answer to three decimal places.
Flag question: Question 6Question 60.5 pts
Calculate the z score for Udonis Haslem. Round your answer to three decimal places.
Flag question: Question 7Question 70.5 pts
Calculate the z score for Chris Silva. Round your answer to three decimal places.
Flag question: Question 8Question 80.5 pts
Calculate the z score for Haywood Highsmith. Round your answer to three decimal places.
Flag question: Question 9Question 90.5 pts
Calculate the z-score for Omer Yurtseven. Round your answer to three decimal places.
Flag question: Question 10Question 102 pts
If you randomly select a professional basketball player, what is the probability that the player’s average points per game is between Chris Silva and Tyler Herro?
To answer this question you need to use the table in the appendix of the text to figure out the area between those two scores on the normal curve. Show your work on this. To get full credit, you must demonstrate all calculations, values you used from the appendix, and steps you took to get your answer (that is, your answer must include the z score, the area under the curve that you found in the appendix, and how you came to your final answer).
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Flag question: Question 11Question 112 pts
If you randomly select an NBA player, what percentage of the time would the player’s average points per game be less than Marcus Garrett’s record of points per game?
To answer this question you need to use the table in the appendix of the text to figure out the area below this score. Show your work on this. To get full credit, you must demonstrate all calculations, values you used from the appendix, and steps you took to get your answer (that is, your answer must include the z score, the area under the curve that you found in the appendix, and how you came to your final answer).
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Flag question: Question 12Question 121.5 pts
You and your friend are engaging in a classic sports argument: which famous athlete is better at their respective sport? In other words, we’re going to explore the question: in the year 2021, was Jimmy Butler better at basketball than Tom Brady was at football? Because we’re comparing to totally different sports with different statistics, in order to answer this question, we need to look at standardized scores (z-scores).
For Tom Brady, we’ll look at passing yards. Passing yards are a good way to measure a quarterback’s ability to move the ball (in short, higher average passing yards per game is a good thing). For Jimmy Butler, we can look at average points per game.
In the 2021 season, Tom Brady had an average of 312.7 passing yards per game. The total league average for the quarterbacks in the NFL was 162.86 with a standard deviation of 95.98.
Using this information tell me, who was better in 2020: Tom Brady or Jimmy Butler and why?
In your answer include the following information:
The z scores for Tom Brady’s passing yards and Jimmy Butler’s points per game (Hint: you already calculated the z score for Jimmy Butler’s points per game in the questions above).
A comparison of the two z scores an explanation of your conclusion, based on those z-scores. What is your final conclusion: who is better, relative to others in their respective sports? Why?
