The average amount of money spent for lunch per person in the college cafeteria is $7.33 and the standard deviation is $2.2. Suppose that 13 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere possible. a. What is the distribution of X? X - N 7.33 2.2 88 b. What is the distribution of ? N 7.33 ✓0.6102 ✓ c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $8.0247 and $8.4798. d. For the group of 13 patrons, find the probability that the average lunch cost is between $8.0247 am $8.4798. normal necessary? Not of e. For part d), is the assumption that the distribution
The average amount of money spent for lunch per person in the college cafeteria is $7.33 and the standard deviation is $2.2. Suppose that 13 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere possible. a. What is the distribution of X? X - N 7.33 2.2 88 b. What is the distribution of ? N 7.33 ✓0.6102 ✓ c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $8.0247 and $8.4798. d. For the group of 13 patrons, find the probability that the average lunch cost is between $8.0247 am $8.4798. normal necessary? Not of e. For part d), is the assumption that the distribution
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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![**Understanding the Distribution of Lunch Costs in a College Cafeteria**
The average amount of money spent for lunch per person in the college cafeteria is $7.33 and the standard deviation is $2.2. Suppose that 13 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
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**Questions and Analysis:**
a. **What is the distribution of \(X\)?**
\(X \sim N(7.33, 2.2)\)
b. **What is the distribution of \(\bar{X}\)?**
\(\bar{X} \sim N(7.33, 0.6102)\)
c. **For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $8.0247 and $8.4798.**
*[The answer should be calculated based on the normal distribution given in part (a).]*
d. **For the group of 13 patrons, find the probability that the average lunch cost is between $8.0247 and $8.4798.**
*[The answer should be calculated based on the normal distribution of the sample mean given in part (b).]*
e. **For part (d), is the assumption that the distribution is normal necessary?**
*[Answer to be selected:]*
- \( \bigcirc \) Yes
- \( \bigcirc \) No
---
**Hint:**
- **Hint:** [Link to Hint]
- **Textbook Pages:** [Link to Textbook Pages]
---
**Submit Question:**
*Button to submit the answer.*
---
In this analysis, we explore the distribution and probability of lunch costs for individual patrons as well as the average cost for a group using normal distribution principles. The importance of normality assumption is also emphasized in the context of statistical evaluation.
---
**Explanation of Graphs/Diagrams:**
*This section contains placeholders for graphs or diagrams if there are any to be included from statistical tables, normal distribution curves, or sample distribution diagrams, which help in visual understanding of the data and probability calculations.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba867a91-7946-4dc8-8b92-57b0d80fa10e%2Ff37d9918-5d51-4412-82c7-f1cad2fd691c%2Fz1lf1z5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Distribution of Lunch Costs in a College Cafeteria**
The average amount of money spent for lunch per person in the college cafeteria is $7.33 and the standard deviation is $2.2. Suppose that 13 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
---
**Questions and Analysis:**
a. **What is the distribution of \(X\)?**
\(X \sim N(7.33, 2.2)\)
b. **What is the distribution of \(\bar{X}\)?**
\(\bar{X} \sim N(7.33, 0.6102)\)
c. **For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $8.0247 and $8.4798.**
*[The answer should be calculated based on the normal distribution given in part (a).]*
d. **For the group of 13 patrons, find the probability that the average lunch cost is between $8.0247 and $8.4798.**
*[The answer should be calculated based on the normal distribution of the sample mean given in part (b).]*
e. **For part (d), is the assumption that the distribution is normal necessary?**
*[Answer to be selected:]*
- \( \bigcirc \) Yes
- \( \bigcirc \) No
---
**Hint:**
- **Hint:** [Link to Hint]
- **Textbook Pages:** [Link to Textbook Pages]
---
**Submit Question:**
*Button to submit the answer.*
---
In this analysis, we explore the distribution and probability of lunch costs for individual patrons as well as the average cost for a group using normal distribution principles. The importance of normality assumption is also emphasized in the context of statistical evaluation.
---
**Explanation of Graphs/Diagrams:**
*This section contains placeholders for graphs or diagrams if there are any to be included from statistical tables, normal distribution curves, or sample distribution diagrams, which help in visual understanding of the data and probability calculations.*
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