Homework Help is Here – Start Your Trial Now!
Math
Statistics
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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
100%
Help with c and d
**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.*
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.*
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS