Please label each part # Understanding the Distribution of Fly Ball Distances in Baseball## OverviewSuppose that the distance of fly balls hit to the outfield in baseball is normally distributed with a mean of 234 feet and a standard deviation of 54 feet. We randomly sample 49 fly balls to analyze their distribution.### Part (a)**Objective:** Determine the distribution of the average distance (in feet) for 49 fly balls.Given:- Mean (μ) = 234 feet- Standard deviation (σ) = 54 feet- Sample size (n) = 49The distribution of the sample mean $ \bar{X} $ is normally distributed with:- Mean = μ- Standard deviation = $ \frac{σ}{\sqrt{n}} $Calculate and round the standard deviation to two decimal places.### Part (b)**Objective:** Calculate the probability that the 49 fly balls traveled an average of less than 226 feet.- Find $ P(\bar{X} < 226) $.- Round your answer to four decimal places.**Graphical Representation:**- Four normal distribution graphs are presented.- The graph with the correct shaded area corresponds to the lower tail of the normal distribution up to 226 feet.### Part (c)**Objective:** Find the 80th percentile of the distribution of the average distance of 49 fly balls.- Calculate the value corresponding to the 80th percentile.- Round your answer to two decimal places.These exercises help in understanding the application of normal distribution concepts and how to calculate probabilities and percentiles from a sample.

Given Information: The distance of fly balls to the outfield is normally distributed with mean μ=234…

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 234 feet and a standard deviation of 54 feet. We randomly sample 49 fly balls. O Part (a) If X = average distance in feet for 49 fly balls, then give the distribution of X. Round your standard deviation to two decimal places. X - O Part (b) What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.) Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability.

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 234 feet and a standard deviation of 54 feet. We randomly sample 49 fly balls. O Part (a) If X = average distance in feet for 49 fly balls, then give the distribution of X. Round your standard deviation to two decimal places. X - O Part (b) What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.) Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability.

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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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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Please label each part

# Understanding the Distribution of Fly Ball Distances in Baseball

## Overview

Suppose that the distance of fly balls hit to the outfield in baseball is normally distributed with a mean of 234 feet and a standard deviation of 54 feet. We randomly sample 49 fly balls to analyze their distribution.

### Part (a)

**Objective:** Determine the distribution of the average distance (in feet) for 49 fly balls.

Given:
- Mean (μ) = 234 feet
- Standard deviation (σ) = 54 feet
- Sample size (n) = 49

The distribution of the sample mean $ \bar{X} $ is normally distributed with:
- Mean = μ
- Standard deviation = $ \frac{σ}{\sqrt{n}} $

Calculate and round the standard deviation to two decimal places.

### Part (b)

**Objective:** Calculate the probability that the 49 fly balls traveled an average of less than 226 feet.

- Find $ P(\bar{X} < 226) $.
- Round your answer to four decimal places.

**Graphical Representation:**
- Four normal distribution graphs are presented.
- The graph with the correct shaded area corresponds to the lower tail of the normal distribution up to 226 feet.

### Part (c)

**Objective:** Find the 80th percentile of the distribution of the average distance of 49 fly balls.

- Calculate the value corresponding to the 80th percentile.
- Round your answer to two decimal places.

These exercises help in understanding the application of normal distribution concepts and how to calculate probabilities and percentiles from a sample.

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