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Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean u = 92.12 mph and a standard deviation of o = 2.43 mph. 85 90 100 speed (mph) Compute the z-score of pitch with speed 91.4 mph. (Round your answer to two decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds between 88 mph and 94.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds above 94.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 21% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 21%? (Round your answer to the nearest 0.1 mph.) mph

Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean u = 92.12 mph and a standard deviation of o = 2.43 mph. 85 90 100 speed (mph) Compute the z-score of pitch with speed 91.4 mph. (Round your answer to two decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds between 88 mph and 94.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds above 94.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 21% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 21%? (Round your answer to the nearest 0.1 mph.) mph

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean u = 92.12 mph and a standard deviation of o = 2.43 mph. 90 95 100 speed (mph) Compute the Z-score of pitch with speed 91.4 mph. (Round your answer to two decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds between 88 mph and 94.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds above 94.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 21% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 21%? (Round your answer to the nearest 0.1 mph.) mph
Transcribed Image Text:Major League Baseball now records information about every pitch thrown in every game of every season. Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean u = 92.12 mph and a standard deviation of o = 2.43 mph. 90 95 100 speed (mph) Compute the Z-score of pitch with speed 91.4 mph. (Round your answer to two decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds between 88 mph and 94.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds above 94.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 21% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 21%? (Round your answer to the nearest 0.1 mph.) mph
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