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) =
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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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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