### Bearing Lifetime Observations and Normal Probability Plot Coordination**Consider the following n = 10 observations on bearing lifetime (in hours):**152.7, 172.0, 172.5, 173.3, 193.0, 204.7, 216.5, 234.9, 262.6, 422.6To plot these observations on a normal probability plot, you need to determine the coordinates for each data point. This ensures you can visually assess if the data approximates a normal distribution.**Step-by-Step Guide to Plot the Point for 262.6:**1. **Order the Data**: Rank the observations from smallest to largest. The ordered list is: - 152.7, 172.0, 172.5, 173.3, 193.0, 204.7, 216.5, 234.9, 262.6, 422.62. **Calculate the Position**: To find the position of 262.6 in this list: - 262.6 is 9th in the sorted order.3. **Determine the Rank (i)** and **Proportion**: - Rank (i) = 9 - Proportion $ P_i = \frac{i - 0.5}{n} $ - Here, $ n = 10 $ (total number of observations). - Thus, $ P_9 = \frac{9 - 0.5}{10} = \frac{8.5}{10} = 0.85 $4. **Find the Z-Score for the Proportion**: - Use a standard normal distribution table to find the z-score corresponding to a cumulative probability of 0.85. - The z-score for P = 0.85 is approximately 1.036.5. **Coordinate for Normal Probability Plot**: - The x-coordinate is the z-score, and the y-coordinate is the observation value. - Therefore, the coordinates for the point 262.6 are (1.036, 262.6).By following these steps, you generate the coordinates to plot 262.6 on a normal probability plot, which helps in analyzing the distribution pattern of bearing lifetime data.**Final Coordinates for the Point 262.6:**\[ (1.036,

Using the given data, it is been asked to identify the coordinates of point to be plotted on normal…

Consider the following n= 10 observations on bearing lifetime (in hours): 152.7 172.0 172.5 173.3 193.0 204.7 216.5 234.9 262.6 422.6 List the coordinates of the point you would plot on a normal probability plot for the point 262.6:

Consider the following n= 10 observations on bearing lifetime (in hours): 152.7 172.0 172.5 173.3 193.0 204.7 216.5 234.9 262.6 422.6 List the coordinates of the point you would plot on a normal probability plot for the point 262.6:

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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### Bearing Lifetime Observations and Normal Probability Plot Coordination

**Consider the following n = 10 observations on bearing lifetime (in hours):**

152.7, 172.0, 172.5, 173.3, 193.0, 204.7, 216.5, 234.9, 262.6, 422.6

To plot these observations on a normal probability plot, you need to determine the coordinates for each data point. This ensures you can visually assess if the data approximates a normal distribution.

**Step-by-Step Guide to Plot the Point for 262.6:**

1. **Order the Data**: Rank the observations from smallest to largest. The ordered list is:
- 152.7, 172.0, 172.5, 173.3, 193.0, 204.7, 216.5, 234.9, 262.6, 422.6

2. **Calculate the Position**: To find the position of 262.6 in this list:
- 262.6 is 9th in the sorted order.

3. **Determine the Rank (i)** and **Proportion**:
- Rank (i) = 9
- Proportion $ P_i = \frac{i - 0.5}{n} $
- Here, $ n = 10 $ (total number of observations).
- Thus, $ P_9 = \frac{9 - 0.5}{10} = \frac{8.5}{10} = 0.85 $

4. **Find the Z-Score for the Proportion**:
- Use a standard normal distribution table to find the z-score corresponding to a cumulative probability of 0.85.
- The z-score for P = 0.85 is approximately 1.036.

5. **Coordinate for Normal Probability Plot**:
- The x-coordinate is the z-score, and the y-coordinate is the observation value.
- Therefore, the coordinates for the point 262.6 are (1.036, 262.6).

By following these steps, you generate the coordinates to plot 262.6 on a normal probability plot, which helps in analyzing the distribution pattern of bearing lifetime data.

**Final Coordinates for the Point 262.6:**
\[ (1.036,

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