**Analysis of Fastball Speeds in Major League Baseball****Introduction:**Major League Baseball (MLB) now collects data on every pitch thrown in each game of every season. Statistician Jim Albert gathered data from 20 starting pitchers during the 2009 MLB season. The dataset included the types of pitches thrown (curveball, changeup, slider, etc.) and the speeds of the balls as they left the pitcher's hand. Specifically, for this analysis, we look at four-seam fastballs from these pitchers. **Histogram of Pitch Speeds:**The histogram below represents the speeds of 30,740 four-seam fastballs thrown by these pitchers during the 2009 season:[Graph Description]- The x-axis represents the speed of the pitch (in mph), ranging from approximately 83 mph to 100 mph.- The y-axis represents the count, i.e., the number of pitches at each speed.- The distribution of pitches follows a bell curve (normal distribution), clustered around a mean (μ) speed of 92.12 mph with a standard deviation (σ) of 2.43 mph.Given the normal distribution, this data allows for the computation of various statistical values and probabilities.**Statistical Problems:**1. **Z-Score Calculation:** - Compute the z-score for a pitch with a speed of 88.7 mph. - Formula: \[ z = \frac{(X - \mu)}{\sigma} \]2. **Fraction of Four-Seam Fastballs Between Two Speeds:** - Approximate the fraction of four-seam fastballs that have speeds between 91.6 mph and 94.4 mph. - Use the appropriate normal distribution areas.3. **Fraction of Four-Seam Fastballs Below a Certain Speed:** - Approximate the fraction of four-seam fastballs that have speeds below 91.6 mph. - Use the appropriate normal distribution areas.4. **Identifying the Fastest Pitches:** - To identify four-seam fastballs within the fastest 16% of all such pitches, determine the minimum speed required to be in the top 16%. - Using the normal distribution table and given parameters, find this value.Each problem requires understanding of the normal distribution, z-scores, and percentages/probabilities related to the data's distribution.**Exercises:**1. Compute the z

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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. 100 speed (mph) Compute the z-score of pitch with speed 88.7 mph. (Round your answer to two decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds between 91.6 mph and 94.4 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 below 91.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) 000 000z sunos

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. 100 speed (mph) Compute the z-score of pitch with speed 88.7 mph. (Round your answer to two decimal places.) Approximately what fraction of these four-seam fastballs would you expect to have speeds between 91.6 mph and 94.4 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 below 91.6 mph? (Express your answer as a decimal, not a percent, and round to three decimal places.) 000 000z sunos

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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