The average score for games played in the NFL is 21.9 and the standard deviation is 9.3 points. Forty-nine games are randomly selected. Round all answers to four decimal places where possible and assume a normal distribution.a. What is the distribution of \(\overline{x}\)? \(\overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})\)b. What is the distribution of \(\sum x\)? \(\sum x \sim N(n\mu, \sqrt{n}\sigma)\)c. \(P(\overline{x} < 20.3071) =\) d. Find the 60th percentile for the mean score for this sample size.e. \(P(20.0071 < \overline{x} < 23.2643) =\) f. Q1 for the \(\overline{x}\) distribution =g. \(P(\sum x > 999.9479) =\) h. For part c) and e), is the assumption of normal necessary? \( \text{Yes} \) or \( \text{No} \)**Hint:****Some Helpful Videos:**- The Central Limit Theorem for Sums- Finding the Sampling Distribution- Finding the Sampling Distribution for a Sum(Note: Links to the videos are not provided in the image.)Ensure calculations are performed correctly by referring to relevant statistical formulas and theorems.

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The average score for games played in the NFL is 21.9 and the standard deviation is 9.3 points. 49 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of ? - N( b. What is the distribution of x? x- N( c. P(a < 20.3071) =

The average score for games played in the NFL is 21.9 and the standard deviation is 9.3 points. 49 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of ? - N( b. What is the distribution of x? x- N( c. P(a < 20.3071) =

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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