e. Let the sample mean approximate u? And the sample standard deviation approximate o? The distribution of X can then be approximated by X-, f. Use the distribution in part e to calculate the probability that the maximum capacity of sports stadiums is less than 67,000 spectators.
e. Let the sample mean approximate u? And the sample standard deviation approximate o? The distribution of X can then be approximated by X-, f. Use the distribution in part e to calculate the probability that the maximum capacity of sports stadiums is less than 67,000 spectators.
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Hello, I need help with part e and f. I attached a photo of the data set and questions e and f. I calculated the sample mean in excel and got 60,143. For the sample standard deviation, I got 10,462.38.
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### Data Analysis: Maximum Capacity of Sports Stadiums
**e. Let the sample mean approximate μ and the sample standard deviation approximate σ.**
- The distribution of X can then be approximated by \( X \sim N(\mu, \sigma^2) \).
**f. Use the distribution in part e to calculate the probability that the maximum capacity of sports stadiums is less than 67,000 spectators.**
**g. Determine the cumulative relative frequency that the maximum capacity of sports stadiums is less than 67,000 spectators.**
- **Hint:** Order the data and count the sports stadiums that have a maximum capacity less than 67,000. Divide by the total number of sports stadiums in the sample.
**h. Why aren’t the answers to part f and part g exactly the same?**
---
Note: The document is a snippet from a lesson on statistical analysis, focusing on probabilities and cumulative frequencies related to stadium capacities. There are no graphs or diagrams present in the image.
![**Data Analysis: Maximum Capacity**
**Chapter 6 Assignment**
A sample of the maximum capacity of spectators of sports stadiums is included in the table:
| 40,000 | 40,000 | 45,050 | 45,500 | 46,249 | 48,134 |
|--------|--------|--------|--------|--------|--------|
| 49,133 | 50,071 | 50,906 | 50,466 | 50,832 | 51,500 |
| 51,500 | 51,900 | 52,000 | 52,132 | 52,000 | 52,530 |
| 52,692 | 53,864 | 54,000 | 55,000 | 55,000 | 55,000 |
| 55,000 | 55,000 | 55,000 | 55,000 | 55,000 | 58,008 |
| 59,860 | 60,000 | 60,492 | 60,580 | 62,380 | 62,872 |
| 64,035 | 65,000 | 66,647 | 66,000 | 66,161 | 67,428 |
| 68,349 | 68,976 | 69,372 | 70,107 | 70,585 | 71,594 |
| 72,922 | 73,379 | 74,500 | 75,025 | 76,212 | 78,000 |
| 78,000 | 80,000 | 80,000 | 80,000 | 82,300 | |
*The table does not include horse-racing or motor-racing stadiums.*
**a. Calculate the sample mean and the sample standard deviation for the maximum capacity of sports stadiums (see data above).**
**Sample Mean:**
\[
\bar{X} = \frac{\sum_{i=1}^{n} x_{i}}{n}
\]
\[ = \frac{75,339}{78} = 73,859 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e4abf04-5494-4b59-8e86-398eb44a6ecc%2Fcf8bb0cc-bfcc-40b4-a3ca-000639915a97%2Fik9oh9g_processed.png&w=3840&q=75)
Transcribed Image Text:**Data Analysis: Maximum Capacity**
**Chapter 6 Assignment**
A sample of the maximum capacity of spectators of sports stadiums is included in the table:
| 40,000 | 40,000 | 45,050 | 45,500 | 46,249 | 48,134 |
|--------|--------|--------|--------|--------|--------|
| 49,133 | 50,071 | 50,906 | 50,466 | 50,832 | 51,500 |
| 51,500 | 51,900 | 52,000 | 52,132 | 52,000 | 52,530 |
| 52,692 | 53,864 | 54,000 | 55,000 | 55,000 | 55,000 |
| 55,000 | 55,000 | 55,000 | 55,000 | 55,000 | 58,008 |
| 59,860 | 60,000 | 60,492 | 60,580 | 62,380 | 62,872 |
| 64,035 | 65,000 | 66,647 | 66,000 | 66,161 | 67,428 |
| 68,349 | 68,976 | 69,372 | 70,107 | 70,585 | 71,594 |
| 72,922 | 73,379 | 74,500 | 75,025 | 76,212 | 78,000 |
| 78,000 | 80,000 | 80,000 | 80,000 | 82,300 | |
*The table does not include horse-racing or motor-racing stadiums.*
**a. Calculate the sample mean and the sample standard deviation for the maximum capacity of sports stadiums (see data above).**
**Sample Mean:**
\[
\bar{X} = \frac{\sum_{i=1}^{n} x_{i}}{n}
\]
\[ = \frac{75,339}{78} = 73,859 \]
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