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 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. This study showed that the speeds of fastballs forms a normal distribution with mean μ = 92.12 mph and a standard deviation of σ = 2.43 mph. Compute the z-score of pitch with speed 98.1 mph. (Round your answer to two decimal places.) Approximately what fraction of these fastballs would you expect to have speeds between 90 mph and 98 mph? (Express your answer as a decimal, not a percent, and round to at least three decimal places.) Approximately what fraction of these fastballs would you expect to have speeds above 98 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 slowest 22% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 22%? (Round your answer to the nearest tenth of a mph.)

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 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. This study showed that the speeds of fastballs forms a normal distribution with mean μ = 92.12 mph and a standard deviation of σ = 2.43 mph.

Compute the z-score of pitch with speed 98.1 mph. (Round your answer to two decimal places.)

Approximately what fraction of these fastballs would you expect to have speeds between 90 mph and 98 mph? (Express your answer as a decimal, not a percent, and round to at least three decimal places.)

Approximately what fraction of these fastballs would you expect to have speeds above 98 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 slowest 22% of all such pitches. Below what speed must a four-seam fastball be in order to be included in the slowest 22%? (Round your answer to the nearest tenth of a mph.)

In the box below, type in what you entered into the calculator to get your answers for each question. If you used the online Statistics Calcuator, indicate the screens used, and any values of input variables.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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