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
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![### 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
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