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. What is the distribution of x? - N 21.2 2.2556) o or b. What is the distribution of Σα? Σα N( 360.4 38.344✔ or or c. P(> 19.1166) = 0.8212 ✓ d. Find the 79th percentile for the mean score for this sample size. 23.018✔ OF e. P(19.8166 < x < 22.7278) = 0.4808 f. Q1 for the distribution: = g. P x > 408.2822) = h. For part c) and e), is the assumption of normal necessary? No Yes o
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. What is the distribution of x? - N 21.2 2.2556) o or b. What is the distribution of Σα? Σα N( 360.4 38.344✔ or or c. P(> 19.1166) = 0.8212 ✓ d. Find the 79th percentile for the mean score for this sample size. 23.018✔ OF e. P(19.8166 < x < 22.7278) = 0.4808 f. Q1 for the distribution: = g. P x > 408.2822) = h. For part c) and e), is the assumption of normal necessary? No Yes o
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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F AND G ONLY PLEASE
![**Statistical Analysis in NFL Games**
The average score for games played in the NFL is 21.2 and the standard deviation is 9.3 points. In this analysis, 17 games are randomly selected for evaluation. All answers are rounded to four decimal places, and a normal distribution is assumed throughout.
**a. Distribution of the Sample Mean (\(\bar{x}\))**
The sample mean \(\bar{x}\) follows a normal distribution with the parameters:
\[ \bar{x} \sim N(21.2, 2.2556) \]
**b. Distribution of the Sum of Scores (\(\sum x\))**
The sum of scores \(\sum x\) follows a normal distribution with the parameters:
\[ \sum x \sim N(360.4, 38.344) \]
**c. Probability Calculation**
The probability that the sample mean (\(\bar{x}\)) is greater than 19.1166 is:
\[ P(\bar{x} > 19.1166) = 0.8212 \]
**d. 79th Percentile of the Sample Mean**
The 79th percentile for the mean score for this sample size is:
\[ \text{Percentile} = 23.018 \]
**e. Probability Within a Range**
The probability that the sample mean (\(\bar{x}\)) falls between 19.8166 and 22.7278 is:
\[ P(19.8166 < \bar{x} < 22.7278) = 0.4808 \]
**f. First Quartile of the Distribution of \(\bar{x}\)**
\[ Q1 \text{ for the } \bar{x} \text{ distribution} = \text{(To be filled by reader)} \]
**g. Probability Calculation for Sum of Scores**
The probability that the sum of scores (\(\sum x\)) is greater than 408.2822 is:
\[ P(\sum x > 408.2822) = \text{(To be filled by reader)} \]
**h. Assumption Check**
For parts c and e, the assumption of normality is indeed necessary.
\[ \text{Normality Assumption: } \boxed{\text{Yes}} \]
**Note:** Ensure the understanding of the normal distribution and how it applies to sample means and sums. The use of Z-scores and standard errors is fundamental](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb954a688-5e54-4f96-9877-503883322f61%2F33ca5a2b-9d45-416c-8ec4-e5c348469ac3%2Fb7oj65t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Statistical Analysis in NFL Games**
The average score for games played in the NFL is 21.2 and the standard deviation is 9.3 points. In this analysis, 17 games are randomly selected for evaluation. All answers are rounded to four decimal places, and a normal distribution is assumed throughout.
**a. Distribution of the Sample Mean (\(\bar{x}\))**
The sample mean \(\bar{x}\) follows a normal distribution with the parameters:
\[ \bar{x} \sim N(21.2, 2.2556) \]
**b. Distribution of the Sum of Scores (\(\sum x\))**
The sum of scores \(\sum x\) follows a normal distribution with the parameters:
\[ \sum x \sim N(360.4, 38.344) \]
**c. Probability Calculation**
The probability that the sample mean (\(\bar{x}\)) is greater than 19.1166 is:
\[ P(\bar{x} > 19.1166) = 0.8212 \]
**d. 79th Percentile of the Sample Mean**
The 79th percentile for the mean score for this sample size is:
\[ \text{Percentile} = 23.018 \]
**e. Probability Within a Range**
The probability that the sample mean (\(\bar{x}\)) falls between 19.8166 and 22.7278 is:
\[ P(19.8166 < \bar{x} < 22.7278) = 0.4808 \]
**f. First Quartile of the Distribution of \(\bar{x}\)**
\[ Q1 \text{ for the } \bar{x} \text{ distribution} = \text{(To be filled by reader)} \]
**g. Probability Calculation for Sum of Scores**
The probability that the sum of scores (\(\sum x\)) is greater than 408.2822 is:
\[ P(\sum x > 408.2822) = \text{(To be filled by reader)} \]
**h. Assumption Check**
For parts c and e, the assumption of normality is indeed necessary.
\[ \text{Normality Assumption: } \boxed{\text{Yes}} \]
**Note:** Ensure the understanding of the normal distribution and how it applies to sample means and sums. The use of Z-scores and standard errors is fundamental
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