a. What is the distribution of x? x ~ N( 5.0877 X b. What is the distribution of Σα? Σ x - N( 360.4 ✔ 1470.3: X c. P(> 19.1166) = 0.8212✓ O d. Find the 79th percentile for the mean score for this sample size. 23.018 OF e. P(19.8166 < x < 22.7278) =
a. What is the distribution of x? x ~ N( 5.0877 X b. What is the distribution of Σα? Σ x - N( 360.4 ✔ 1470.3: X c. P(> 19.1166) = 0.8212✓ O d. Find the 79th percentile for the mean score for this sample size. 23.018 OF e. P(19.8166 < x < 22.7278) =
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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![### NFL Games Score Distribution and 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 \(\bar{x}\)? \(\bar{x} \sim N(\_\_\_\_\, \_\_\_\_\_\_\_\_\,)\)
**Answer:**
\[ \bar{x} \sim N(21.2, 2.255) \quad \text{Incorrect: } 5.0877 \]
#### b. Distribution of the Sum of Scores (\(\sum x\))
**Question:**
What is the distribution of \(\sum x\)? \(\sum x \sim N(\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\,)\)
**Answer:**
\[ \sum x \sim N(360.4, 38.335) \quad \text{Incorrect: } 1470.3 \]
#### c. Probability Calculation
**Question:**
What is \( P(\bar{x} > 19.1166) \)?
**Answer:**
\[ P(\bar{x} > 19.1166) = 0.8212 \]
#### d. Percentile Calculation
**Question:**
Find the 79th percentile for the mean score for this sample size.
**Answer:**
\[ 23.018 \]
#### e. Probability within a Range
**Question:**
What is \( P(19.8166 < \bar{x} < 22.7278) \)?
**Answer:**
\[ \boxed{\phantom{0}} \] *(requires to be filled)*
#### f. First Quartile (Q1) Calculation
**Question:**
Determine Q1 for the \(\bar{x}\) distribution.
**Answer:**
\[ \boxed{\phantom{0}} \] *(requires to be filled)*
#### g. Probability for the Sum of Scores
**Question:**
Calculate \( P\left(\sum x > 408.2822\right) \).
**Answer:**
\[ \boxed{\phantom{0}} \] *(requires to be filled)*
#### h.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb954a688-5e54-4f96-9877-503883322f61%2F01581b1c-24a7-477f-941f-feb69887c30a%2Fy9685ri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### NFL Games Score Distribution and 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 \(\bar{x}\)? \(\bar{x} \sim N(\_\_\_\_\, \_\_\_\_\_\_\_\_\,)\)
**Answer:**
\[ \bar{x} \sim N(21.2, 2.255) \quad \text{Incorrect: } 5.0877 \]
#### b. Distribution of the Sum of Scores (\(\sum x\))
**Question:**
What is the distribution of \(\sum x\)? \(\sum x \sim N(\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\,)\)
**Answer:**
\[ \sum x \sim N(360.4, 38.335) \quad \text{Incorrect: } 1470.3 \]
#### c. Probability Calculation
**Question:**
What is \( P(\bar{x} > 19.1166) \)?
**Answer:**
\[ P(\bar{x} > 19.1166) = 0.8212 \]
#### d. Percentile Calculation
**Question:**
Find the 79th percentile for the mean score for this sample size.
**Answer:**
\[ 23.018 \]
#### e. Probability within a Range
**Question:**
What is \( P(19.8166 < \bar{x} < 22.7278) \)?
**Answer:**
\[ \boxed{\phantom{0}} \] *(requires to be filled)*
#### f. First Quartile (Q1) Calculation
**Question:**
Determine Q1 for the \(\bar{x}\) distribution.
**Answer:**
\[ \boxed{\phantom{0}} \] *(requires to be filled)*
#### g. Probability for the Sum of Scores
**Question:**
Calculate \( P\left(\sum x > 408.2822\right) \).
**Answer:**
\[ \boxed{\phantom{0}} \] *(requires to be filled)*
#### h.
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