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Finding Probabilities in Normal Distributions 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. The data showed that the speeds of the fastballs are normally distributed with mean 92.12 mph and standard deviation 2.43 mph. (a) Compute the z-score of the fastball with speed 89.6 mph. Round your answer to two decimal places. (b) What percentage of these fastballs would you expect to have speeds between 89.2 mph and 93 mph? Express your answer as a decimal. Round to three decimal places. (c) What percentage of these fastballs would you expect to have speeds above 93 mph? Express your answer as a decimal. Round to three decimal places. (d) Finding Values: A baseball fan wishes to identify the fastballs among the fastest 21% of all such pitches. Above what speed must a fastball be in order to be included in the fastest 21%? Round your answer to the nearest 0.1 mph. mph

Finding Probabilities in Normal Distributions 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. The data showed that the speeds of the fastballs are normally distributed with mean 92.12 mph and standard deviation 2.43 mph. (a) Compute the z-score of the fastball with speed 89.6 mph. Round your answer to two decimal places. (b) What percentage of these fastballs would you expect to have speeds between 89.2 mph and 93 mph? Express your answer as a decimal. Round to three decimal places. (c) What percentage of these fastballs would you expect to have speeds above 93 mph? Express your answer as a decimal. Round to three decimal places. (d) Finding Values: A baseball fan wishes to identify the fastballs among the fastest 21% of all such pitches. Above what speed must a 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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Finding Probabilities in Normal Distributions 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. The data showed that the speeds of the fastballs are normally distributed with mean 92.12 mph and standard deviation 2.43 mph. (a) Compute the z-score of the fastball with speed 89.6 mph. Round your answer to two decimal places. (b) What percentage of these fastballs would you expect to have speeds between 89.2 mph and 93 mph? Express your answer as a decimal. Round to three decimal places. (c) What percentage of these fastballs would you expect to have speeds above 93 mph? Express your answer as a decimal. Round to three decimal places. (d) Finding Values: A baseball fan wishes to identify the fastballs among the fastest 21% of all such pitches. Above what speed must a fastball be in order to be included in the fastest 21%? Round your answer to the nearest 0.1 mph. mph Question Help: Message instructor Submit Question
Transcribed Image Text:Finding Probabilities in Normal Distributions 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. The data showed that the speeds of the fastballs are normally distributed with mean 92.12 mph and standard deviation 2.43 mph. (a) Compute the z-score of the fastball with speed 89.6 mph. Round your answer to two decimal places. (b) What percentage of these fastballs would you expect to have speeds between 89.2 mph and 93 mph? Express your answer as a decimal. Round to three decimal places. (c) What percentage of these fastballs would you expect to have speeds above 93 mph? Express your answer as a decimal. Round to three decimal places. (d) Finding Values: A baseball fan wishes to identify the fastballs among the fastest 21% of all such pitches. Above what speed must a fastball be in order to be included in the fastest 21%? Round your answer to the nearest 0.1 mph. mph Question Help: Message instructor Submit Question
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