The average score for games played in the NFL is 20.9 and the standard deviation is 9.3 points. 18 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of x? x ~ N( 20.9 9.3 X) 0 b. What is the distribution of Σx? Σ - N( X 376.2, 1556.8 x) o c. P( 23.112) = 0.8438✔ 0 < d. Find the 60th percentile for the mean score for this sample size. 21.469 x e. P(21.512 < x < 22.196) = 0.1121 OF f. Q1 for the distribution = 19.4204 X g. Pa x > 423.216) = 0.1170 h. For part c) and e), is the assumption of normal necessary? No Yes می
The average score for games played in the NFL is 20.9 and the standard deviation is 9.3 points. 18 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of x? x ~ N( 20.9 9.3 X) 0 b. What is the distribution of Σx? Σ - N( X 376.2, 1556.8 x) o c. P( 23.112) = 0.8438✔ 0 < d. Find the 60th percentile for the mean score for this sample size. 21.469 x e. P(21.512 < x < 22.196) = 0.1121 OF f. Q1 for the distribution = 19.4204 X g. Pa x > 423.216) = 0.1170 h. For part c) and e), is the assumption of normal necessary? No Yes می
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
F ONLY PLEASE
![### Statistics in NFL Game Scores
The average score for games played in the NFL is known to be 20.9, with a standard deviation of 9.3 points. In a statistical analysis, 18 games are randomly selected. All answers are rounded to four decimal places, and a normal distribution is assumed.
#### Questions and Solutions
**a. What is the distribution of \(\bar{x}\)?**
\[
\bar{x} \sim N(20.9, \frac{9.3}{\sqrt{18}})
\]
**Solution:**
\[
\bar{x} \sim N(20.9, 2.1925) \quad \textcolor{green}{\checkmark}
\]
**b. What is the distribution of \(\sum x\)?**
\[
\sum x \sim N(18 \times 20.9, 18 \times 9.3^2)
\]
**Solution:**
\[
\sum x \sim N(376.2, 1556.76) \quad \textcolor{green}{\checkmark}
\]
**c. \(\text{P}(\bar{x} < 23.112) = ?\)**
**Solution:**
\[
\text{P}(\bar{x} < 23.112) = 0.8438 \quad \textcolor{green}{\checkmark}
\]
**d. Find the 60th percentile for the mean score for this sample size.**
**Solution:**
\[
60\text{th percentile} = 21.1658 \quad \textcolor{red}{\times}
\]
**e. \(\text{P}(21.512 < \bar{x} < 22.196) = ?\)**
**Solution:**
\[
\text{P}(21.512 < \bar{x} < 22.196) = 0.1121 \quad \textcolor{green}{\checkmark}
\]
**f. Q1 for the \(\bar{x}\) distribution.**
**Solution:**
\[
Q1 = 19.4204 \quad \textcolor{red}{\times}
\]
**g. \(\text{P}(\sum x > 423.216) = ?\)**
**Solution:**
\[
\text{P}(\sum](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb954a688-5e54-4f96-9877-503883322f61%2F511e624e-1433-464b-8ebb-62e34aa2224e%2Fe1umw4g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistics in NFL Game Scores
The average score for games played in the NFL is known to be 20.9, with a standard deviation of 9.3 points. In a statistical analysis, 18 games are randomly selected. All answers are rounded to four decimal places, and a normal distribution is assumed.
#### Questions and Solutions
**a. What is the distribution of \(\bar{x}\)?**
\[
\bar{x} \sim N(20.9, \frac{9.3}{\sqrt{18}})
\]
**Solution:**
\[
\bar{x} \sim N(20.9, 2.1925) \quad \textcolor{green}{\checkmark}
\]
**b. What is the distribution of \(\sum x\)?**
\[
\sum x \sim N(18 \times 20.9, 18 \times 9.3^2)
\]
**Solution:**
\[
\sum x \sim N(376.2, 1556.76) \quad \textcolor{green}{\checkmark}
\]
**c. \(\text{P}(\bar{x} < 23.112) = ?\)**
**Solution:**
\[
\text{P}(\bar{x} < 23.112) = 0.8438 \quad \textcolor{green}{\checkmark}
\]
**d. Find the 60th percentile for the mean score for this sample size.**
**Solution:**
\[
60\text{th percentile} = 21.1658 \quad \textcolor{red}{\times}
\]
**e. \(\text{P}(21.512 < \bar{x} < 22.196) = ?\)**
**Solution:**
\[
\text{P}(21.512 < \bar{x} < 22.196) = 0.1121 \quad \textcolor{green}{\checkmark}
\]
**f. Q1 for the \(\bar{x}\) distribution.**
**Solution:**
\[
Q1 = 19.4204 \quad \textcolor{red}{\times}
\]
**g. \(\text{P}(\sum x > 423.216) = ?\)**
**Solution:**
\[
\text{P}(\sum
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman