A sample of 100 cars driving on a freeway during a morning commute was drawn, and the number of occupants in each car was recorded. The results were as follows: Occupants | 1 2 3 4 5 Number of Cars 70 15 10 3 2 а. Find the sample mean number of occupants. b. Find the sample standard deviation of the number of occupants. Find the sample median number of occupants. Compute the first and third quartiles of the number of occupants. What proportion of cars had more than the mean number of occupants? For what proportion of cars was the number of occupants more than one standard deviation greater than the mean? For what proportion of cars was the number of occupants within one standard C. d. е. f. g. deviation of the mean?
A sample of 100 cars driving on a freeway during a morning commute was drawn, and the number of occupants in each car was recorded. The results were as follows: Occupants | 1 2 3 4 5 Number of Cars 70 15 10 3 2 а. Find the sample mean number of occupants. b. Find the sample standard deviation of the number of occupants. Find the sample median number of occupants. Compute the first and third quartiles of the number of occupants. What proportion of cars had more than the mean number of occupants? For what proportion of cars was the number of occupants more than one standard deviation greater than the mean? For what proportion of cars was the number of occupants within one standard C. d. е. f. g. deviation of the mean?
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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Transcribed Image Text:**Title: Analysis of Car Occupancy on a Freeway During Morning Commute**
**Introduction:**
A study was conducted with a sample of 100 cars driving on a freeway during a morning commute. The number of occupants in each car was recorded, and the following data was collected:
**Data Summary:**
| Occupants | 1 | 2 | 3 | 4 | 5 |
|-----------|----|----|----|---|---|
| Number of Cars | 70 | 15 | 10 | 3 | 2 |
**Tasks:**
a. **Sample Mean Calculation:**
- Calculate the sample mean number of occupants.
b. **Sample Standard Deviation Calculation:**
- Determine the sample standard deviation of the number of occupants.
c. **Sample Median Calculation:**
- Find the sample median number of occupants.
d. **Quartile Calculation:**
- Compute the first and third quartiles of the number of occupants.
e. **Proportion Greater than Mean:**
- Identify the proportion of cars that had more than the mean number of occupants.
f. **Proportion More Than One Standard Deviation Above Mean:**
- Determine the proportion of cars where the number of occupants was more than one standard deviation greater than the mean.
g. **Proportion Within One Standard Deviation of Mean:**
- Calculate the proportion of cars where the number of occupants was within one standard deviation of the mean.
**Conclusion:**
This analysis provides detailed insights into the distribution of car occupancy during a morning commute, which can be useful for traffic planning and understanding commuter patterns.
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