Use Excel to find the z-scores that bound the middle 72% of the area under the standard normal curve. Enter the answers in ascending order. Round the answers to two decimal places. The z-scores for the given area are and X +
Use Excel to find the z-scores that bound the middle 72% of the area under the standard normal curve. Enter the answers in ascending order. Round the answers to two decimal places. The z-scores for the given area are and X +
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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![### Finding Z-Scores that Bound the Middle 72% of the Standard Normal Curve using Excel
To find the z-scores that bound the middle 72% of the area under the standard normal curve, you can use Excel. Typically, the steps would involve using the NORM.S.INV() function to find the critical z-scores. Here's a detailed explanation of the process:
1. **Understand the Problem**:
- You need to find the z-scores that capture the middle 72% of the area under the standard normal curve.
- This area is symmetric around the center (mean = 0) of the standard normal distribution.
2. **Calculate the Tail Area**:
- Since the middle 72% is centered, the remaining area in the tails of the distribution is 100% - 72% = 28%.
- Half of this 28% will be in each tail: 28% / 2 = 14% in each tail.
3. **Determine the Z-Scores**:
- The cumulative area to the left of the lower z-score is 0.14.
- The cumulative area to the left of the upper z-score is 0.86 (since 0.14 + 0.72 = 0.86).
4. **Use Excel**:
- In Excel, you can use the NORM.S.INV() function to determine the z-scores.
- For the lower z-score, use `=NORM.S.INV(0.14)`.
- For the upper z-score, use `=NORM.S.INV(0.86)`.
Here is the entry field for the z-scores:
#### The z-scores for the given area are:
\[ \text{Enter the first z-score} \] and \[ \text{Enter the second z-score} \].
Make sure to enter the answers in ascending order and round the answers to two decimal places.
### Example Calculation:
- Suppose the calculation using `=NORM.S.INV(0.14)` in Excel results in -1.08.
- Similarly, suppose the calculation using `=NORM.S.INV(0.86)` results in 1.08.
- The z-scores would be -1.08 and 1.08.
Ensure to check your calculations and press the "Check" button once completed.
---
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Transcribed Image Text:### Finding Z-Scores that Bound the Middle 72% of the Standard Normal Curve using Excel
To find the z-scores that bound the middle 72% of the area under the standard normal curve, you can use Excel. Typically, the steps would involve using the NORM.S.INV() function to find the critical z-scores. Here's a detailed explanation of the process:
1. **Understand the Problem**:
- You need to find the z-scores that capture the middle 72% of the area under the standard normal curve.
- This area is symmetric around the center (mean = 0) of the standard normal distribution.
2. **Calculate the Tail Area**:
- Since the middle 72% is centered, the remaining area in the tails of the distribution is 100% - 72% = 28%.
- Half of this 28% will be in each tail: 28% / 2 = 14% in each tail.
3. **Determine the Z-Scores**:
- The cumulative area to the left of the lower z-score is 0.14.
- The cumulative area to the left of the upper z-score is 0.86 (since 0.14 + 0.72 = 0.86).
4. **Use Excel**:
- In Excel, you can use the NORM.S.INV() function to determine the z-scores.
- For the lower z-score, use `=NORM.S.INV(0.14)`.
- For the upper z-score, use `=NORM.S.INV(0.86)`.
Here is the entry field for the z-scores:
#### The z-scores for the given area are:
\[ \text{Enter the first z-score} \] and \[ \text{Enter the second z-score} \].
Make sure to enter the answers in ascending order and round the answers to two decimal places.
### Example Calculation:
- Suppose the calculation using `=NORM.S.INV(0.14)` in Excel results in -1.08.
- Similarly, suppose the calculation using `=NORM.S.INV(0.86)` results in 1.08.
- The z-scores would be -1.08 and 1.08.
Ensure to check your calculations and press the "Check" button once completed.
---
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