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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 μ = 92.12 mph and a standard deviation of a = 2.43 mph. counts none poos 2000 1000 90 speed (mph) 100 Compute the z-score of pitch with speed 95 mph. (Round your answer to two decimal places.) Find the probability that these four-seam fastballs that you would expect to have speeds between 90.4 mph and 95.8 mph? (Express your answer as a decimal, not a percent, and round to at least 3 decimal places.) mph Find the probability that these four-seam fastballs that you would expect to have speeds below 90.4 mph? (Express your answer as a decimal, not a percent, and round to at least three decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 3% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 3%? (Round your answer to the nearest 0.1 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 μ = 92.12 mph and a standard deviation of a = 2.43 mph. counts none poos 2000 1000 90 speed (mph) 100 Compute the z-score of pitch with speed 95 mph. (Round your answer to two decimal places.) Find the probability that these four-seam fastballs that you would expect to have speeds between 90.4 mph and 95.8 mph? (Express your answer as a decimal, not a percent, and round to at least 3 decimal places.) mph Find the probability that these four-seam fastballs that you would expect to have speeds below 90.4 mph? (Express your answer as a decimal, not a percent, and round to at least three decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 3% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 3%? (Round your answer to the nearest 0.1 mph.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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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 μ = 92.12 mph and a standard deviation of a = 2.43 mph. suno 4000 000€ 2000 1000 85 90 speed (mph) 100 Compute the z-score of pitch with speed 95 mph. (Round your answer to two decimal places.) Find the probability that these four-seam fastballs that you would expect to have speeds between 90.4 mph and 95.8 mph? (Express your answer as a decimal, not a percent, and round to at least 3 decimal places.) mph Find the probability that these four-seam fastballs that you would expect to have speeds below 90.4 mph? (Express your answer as a decimal, not a percent, and round to at least three decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 3% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 3%? (Round your answer to the nearest 0.1 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 μ = 92.12 mph and a standard deviation of a = 2.43 mph. suno 4000 000€ 2000 1000 85 90 speed (mph) 100 Compute the z-score of pitch with speed 95 mph. (Round your answer to two decimal places.) Find the probability that these four-seam fastballs that you would expect to have speeds between 90.4 mph and 95.8 mph? (Express your answer as a decimal, not a percent, and round to at least 3 decimal places.) mph Find the probability that these four-seam fastballs that you would expect to have speeds below 90.4 mph? (Express your answer as a decimal, not a percent, and round to at least three decimal places.) A baseball fan wishes to identify the four-seam fastballs among the fastest 3% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 3%? (Round your answer to the nearest 0.1 mph.)
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