Need to calculate and answer the following short questions, using the table attached.
1- How many players have values that are above the mean in this dataset?
2- How players have values that are below the mean?
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).
4- 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).
5- Calculate the z-score for Haywood Highsmith. 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).
6- 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)
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).
8- Calculate the z-score for Jamal Cain. 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).
9- If you randomly select a professional basketball player, what is the probability that the player’s field goal percentage for the season is between Tyler Herro and Cody Zeller? 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).
10- If you randomly select an NBA player from the whole population, what percentage of the time would the player’s field goal percentage for the season be lower than Duncan Robinson? 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).
11- 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 2023, was Jimmy Butler better at basketball than Travis Kelce (Tight End for Kansas City) 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 Travis Kelce, we’ll look at Yards Per Catch (or Yards Per Reception), which shows the average number of yards a receiver gains every time they catch the football (how far do they take the ball each time they catch it?). It’s a simple but effective metric for evaluating the effectiveness and productivity of a Tight End. In the 2023 season, Travis Kelcy had an average of 10.6 yards per catch. The total NFL average for tight ends that year was 9.77 with a standard deviation of 2.49.
Using this information tell me, who was better at their respective sport: Jimmy Butler or Travis Kelce?
In your answer include the following information:
a. The z scores for Kelce’s yards per catch and Jimmy Butler’s field goal percentage?
b. A comparison of the two z scores and 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?
c. Is this a fair comparison? Why or why not?
