answer the following questions

Do you remember the mean and standard deviation for field goal percentage for the Miami Heat (you calculated them for assignment 6)? 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).

Question 1

How many players have values that are above the mean in this dataset?

How players have values that are below the mean? 13, 6, 12, or 8

Question 3

Calculate the z-score for Bam Adebayo. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Question 4

Calculate the z-score for Dewayne Dedmon. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Question 5

Calculate the z-score for Jimmy Butler. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Question 6

Calculate the z-score for NIkola Jovic. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Question 7

Calculate the z-score for Tyler Herro. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Question 8

Calculate the z-score for Gabe Vincent. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Question 9

Calculate the z-score for Dru Smith. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Question 10

If you randomly select a professional basketball player, what is the probability that the player’s points per game for the season is between Cody Zeller and Udonis Haslim?

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).

Question 11

If you randomly select an NBA player, what percentage of the time would the player’s points per game for the season be less than Tyler Herro’s?

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).

Question 12

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 2022, 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 points per game.

In the 2022 season, Tom Brady had an average of 276.1 passing yards per game. The total league average for the quarterbacks in the NFL was 226.19 with a standard deviation of 37.80

Using this information tell me, who was better: Tom Brady or Jimmy Butler and why?

In your answer include the following information:

1. 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 in the questions above).
2. 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? question 13 Make a post with the following: What did you write for the last question (question 12)—who did you think was better in their respective sport and why? Come up with an example of a time when it would be useful to use a z-score. This must be your own example.