### NFL Game Score Statistics#### Problem Statement:The average score for games played in the National Football League (NFL) is 20.7 points, with a standard deviation of 9.1 points. A random sample of 7 games is selected. For the following questions, round all probabilities to four decimal places where possible, percentiles to two decimal places, and assume a normal distribution.#### Questions:**a. Distribution of the Sample Mean \(\bar{x}\)**Determine the distribution of \(\bar{x}\).\[ \bar{x} \sim N(\_\_\_\_, \_\_\_\_) \]**b. Probability Calculation**Find the probability that the sample mean score \(\bar{x}\) is greater than 24.4408.\[ P(\bar{x} > 24.4408) = \_\_\_\_ \]**c. Percentile Calculation**Find the 90th percentile for the mean score for this sample size. Provide the value rounded to two decimal places.\[ \_\_\_\_ \]**d. Probability Within a Range**Calculate the probability that the sample mean score \(\bar{x}\) lies between 21.5408 and 25.2198.\[ P(21.5408 < \bar{x} < 25.2198) = \_\_\_\_ \]**e. Normal Distribution Assumption**Is the assumption of a normal distribution necessary to solve this problem? - \( \circ \) No- \( \circ \) Yes#### Explanation of Symbols:- \(\bar{x}\): Sample mean- \(N(\mu, \sigma^2)\): Normal distribution with mean \(\mu\) and variance \(\sigma^2\)#### Graphs/Diagrams:This problem does not include specific graphs or diagrams. Instead, it focuses on the calculation and understanding of normal distribution properties and probability within the context of sample means.#### Notes:- When addressing the distribution of \(\bar{x}\), consider the Central Limit Theorem which states that the distribution of the sample mean will be approximately normal if the sample size is sufficiently large.- The standard deviation of the sample mean, also known as the standard error, is calculated by dividing the population standard deviation by the square root of the sample size.This exercise enhances understanding of statistical concepts and their practical application in analyzing and predicting outcomes based on sample data.

As per guideline expert have to answer first 3 subparts only.

The average score for games played in the NFL is 20.7 and the standard deviation is 9.1 point games are randomly selected. Round all probabilities to 4 decimal places where possible, percentiles to 2 decimal places and assume a normal distribution. a. What is the distribution of ? ~ N( b. P(E > 24.4408) = c. Find the 90th percentile for the mean score for this sample size. d. P(21.5408 < T < 25.2198) =| e. Is the assumption of normal necessary for this problem? ONOO Yes

The average score for games played in the NFL is 20.7 and the standard deviation is 9.1 point games are randomly selected. Round all probabilities to 4 decimal places where possible, percentiles to 2 decimal places and assume a normal distribution. a. What is the distribution of ? ~ N( b. P(E > 24.4408) = c. Find the 90th percentile for the mean score for this sample size. d. P(21.5408 < T < 25.2198) =| e. Is the assumption of normal necessary for this problem? ONOO Yes

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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