Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. A professional sports team evaluates potential players for a certain position based on two main characteristics, speed and strength. a. Speed is measured by the time required to run a distance of 40 yards, with smaller times indicating more desirable (faster) speeds. From previous speed data for all players in this position, the times to run 40 yards have a mean of 4.60 seconds and a standard deviation of 0.15 seconds, with a minimum time of 4.40 seconds, as shown in the table below. Mean Standard Deviation Minimum Time to run 40 yards | 4.60 seconds 0.15 seconds 4.40 seconds Based on the relationship between the mean, standard deviation, and minimum time, is it reasonable to believe that the distribution of 40-yard running times is approximately normal? Explain. b. Strength is measured by the amount of weight lifted, with more weight indicating more desirable (greater) strength. From previous strength data for all players in this position, the amount of weight lifted has a mean of 310 pounds and a standard deviation of 25 pounds, as shown in the table below. Mean Standard Deviation Amount of weight lifted 310 pounds 25 pounds Calculate and interpret the z-score for a player in this position who can lift a weight of 370 pounds. c. The characteristics of speed and strength are considered to be of equal importance to the team in selecting a player for the position. Based on the information about the means and standard deviations of the speed and strength data for all players and the measurements listed in the table below for Players A and B, which player should the team select if the team can only select one of the two players? Justify your answer. Player A Player B Time to run 40 yards 4.42 seconds | 4.57 seconds Amount of weight lifted | 370 pounds 375 pounds
Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. A professional sports team evaluates potential players for a certain position based on two main characteristics, speed and strength. a. Speed is measured by the time required to run a distance of 40 yards, with smaller times indicating more desirable (faster) speeds. From previous speed data for all players in this position, the times to run 40 yards have a mean of 4.60 seconds and a standard deviation of 0.15 seconds, with a minimum time of 4.40 seconds, as shown in the table below. Mean Standard Deviation Minimum Time to run 40 yards | 4.60 seconds 0.15 seconds 4.40 seconds Based on the relationship between the mean, standard deviation, and minimum time, is it reasonable to believe that the distribution of 40-yard running times is approximately normal? Explain. b. Strength is measured by the amount of weight lifted, with more weight indicating more desirable (greater) strength. From previous strength data for all players in this position, the amount of weight lifted has a mean of 310 pounds and a standard deviation of 25 pounds, as shown in the table below. Mean Standard Deviation Amount of weight lifted 310 pounds 25 pounds Calculate and interpret the z-score for a player in this position who can lift a weight of 370 pounds. c. The characteristics of speed and strength are considered to be of equal importance to the team in selecting a player for the position. Based on the information about the means and standard deviations of the speed and strength data for all players and the measurements listed in the table below for Players A and B, which player should the team select if the team can only select one of the two players? Justify your answer. Player A Player B Time to run 40 yards 4.42 seconds | 4.57 seconds Amount of weight lifted | 370 pounds 375 pounds
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 3P
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Transcribed Image Text:Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results
and explanations.
A professional sports team evaluates potential players for a certain position based on two main characteristics, speed and strength.
a. Speed is measured by the time required to run a distance of 40 yards, with smaller times indicating more desirable (faster) speeds. From previous speed data for all players in this position,
the times to run 40 yards have a mean of 4.60 seconds and a standard deviation of 0.15 seconds, with a minimum time of 4.40 seconds, as shown in the table below.
Mean
Standard Deviation
Minimum
Time to run 40 yards | 4.60 seconds
0.15 seconds
4.40 seconds
Based on the relationship between the mean, standard deviation, and minimum time, is it reasonable to believe that the distribution of 40-yard running times is approximately normal?
Explain.
b. Strength is measured by the amount of weight lifted, with more weight indicating more desirable (greater) strength. From previous strength data for all players in this position, the amount of
weight lifted has a mean of 310 pounds and a standard deviation of 25 pounds, as shown in the table below.
Mean
Standard Deviation
Amount of weight lifted
310 pounds
25 pounds
Calculate and interpret the z-score for a player in this position who can lift a weight of 370 pounds.
c. The characteristics of speed and strength are considered to be of equal importance to the team in selecting a player for the position. Based on the information about the means and
standard deviations of the speed and strength data for all players and the measurements listed in the table below for Players A and B, which player should the team select if the team can
only select one of the two players? Justify your answer.
Player A
Player B
Time to run 40 yards
4.42 seconds | 4.57 seconds
Amount of weight lifted | 370 pounds
375 pounds
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