a. What is the distribution of ? x ~ NO - 5.0877 X b. What is the distribution of Σ? Σ - N( x 360.41470.3: X OB c. P(> 19.1166) = 0.8212 0.8212✔ OF
a. What is the distribution of ? x ~ NO - 5.0877 X b. What is the distribution of Σ? Σ - N( x 360.41470.3: X OB c. P(> 19.1166) = 0.8212 0.8212✔ OF
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
![### NFL Game Scores Statistical Analysis
The average score for games played in the NFL is 21.2 and the standard deviation is 9.3 points. 17 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.
#### a. Distribution of the Sample Mean \( \bar{x} \)
**Question:** What is the distribution of \( \bar{x} \)?
\[ \bar{x} \sim N( \_\_\_\_ , 5.0877 \times) \]
#### b. Distribution of the Sum of Scores \( \sum x \)
**Question:** What is the distribution of \( \sum x \)?
\[ \sum x \sim N(360.4 \checkmark , 1470.3 \times) \]
#### c. Probability Calculation
**Question:** \( P(\bar{x} > 19.1166) = ? \)
\[ P(\bar{x} > 19.1166) = 0.8212 \checkmark \]
#### d. 79th Percentile Calculation
**Question:** Find the 79th percentile for the mean score for this sample size.
\[ 23.018 \checkmark \]
#### e. Probability Interval Calculation
**Question:** \( P(19.8166 < \bar{x} < 22.7278) = ? \)
\[ \_\_\_\_ \]
#### f. First Quartile of \( \bar{x} \)
**Question:** \( Q1 \) for the \( \bar{x} \) distribution:
\[ \_\_\_\_ \]
#### g. Probability Calculation for Sum
**Question:** \( P(\sum x > 408.2822) = ? \)
\[ \_\_\_\_ \]
#### h. Assumption of Normality
**Question:** For part (c) and (e), is the assumption of normal necessary?
\[ \bigcirc \text{ No} \quad \bigcirc \text{ Yes} \]
### Explanation of Diagrams
There are text boxes containing numbers, some of which are marked correct (\checkmark) and some incorrect (\times). Graphs or diagrams are not present in this image. Textual symbols such as \( N \) indicate normal distribution parameters needed for statistical calculations. These references will aid learners in understanding the general and specific distributions of the data under a normality assumption.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb954a688-5e54-4f96-9877-503883322f61%2F86cdbd4c-dede-44e3-8a47-bebd88477d92%2F2inmtyr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### NFL Game Scores Statistical Analysis
The average score for games played in the NFL is 21.2 and the standard deviation is 9.3 points. 17 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.
#### a. Distribution of the Sample Mean \( \bar{x} \)
**Question:** What is the distribution of \( \bar{x} \)?
\[ \bar{x} \sim N( \_\_\_\_ , 5.0877 \times) \]
#### b. Distribution of the Sum of Scores \( \sum x \)
**Question:** What is the distribution of \( \sum x \)?
\[ \sum x \sim N(360.4 \checkmark , 1470.3 \times) \]
#### c. Probability Calculation
**Question:** \( P(\bar{x} > 19.1166) = ? \)
\[ P(\bar{x} > 19.1166) = 0.8212 \checkmark \]
#### d. 79th Percentile Calculation
**Question:** Find the 79th percentile for the mean score for this sample size.
\[ 23.018 \checkmark \]
#### e. Probability Interval Calculation
**Question:** \( P(19.8166 < \bar{x} < 22.7278) = ? \)
\[ \_\_\_\_ \]
#### f. First Quartile of \( \bar{x} \)
**Question:** \( Q1 \) for the \( \bar{x} \) distribution:
\[ \_\_\_\_ \]
#### g. Probability Calculation for Sum
**Question:** \( P(\sum x > 408.2822) = ? \)
\[ \_\_\_\_ \]
#### h. Assumption of Normality
**Question:** For part (c) and (e), is the assumption of normal necessary?
\[ \bigcirc \text{ No} \quad \bigcirc \text{ Yes} \]
### Explanation of Diagrams
There are text boxes containing numbers, some of which are marked correct (\checkmark) and some incorrect (\times). Graphs or diagrams are not present in this image. Textual symbols such as \( N \) indicate normal distribution parameters needed for statistical calculations. These references will aid learners in understanding the general and specific distributions of the data under a normality assumption.
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 with 1 images
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