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Use Excel to find the z-scores that bound the middle 90% 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 S

Use Excel to find the z-scores that bound the middle 90% 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 S

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
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### Using Excel to Find Z-Scores for the Middle 90% of the Standard Normal Curve In this lesson, we'll use Excel to determine the z-scores that bound the middle 90% of the area under the standard normal curve. To do this, follow these steps: 1. **Understanding Z-scores**: Z-scores tell you how many standard deviations an element is from the mean. For the standard normal distribution, the mean is 0 and the standard deviation is 1. 2. **Target Area**: We need the middle 90%, which means we leave out 5% on each tail of the distribution curve. 3. **Using Excel for Calculation**: Excel has built-in functions to find these z-scores. Specifically, we will use the `NORM.S.INV` function, which returns the z-score corresponding to a given cumulative probability. 4. **Finding the Cumulative Probabilities**: - Since we need the middle 90%, we focus on the tail areas first: \( \text{5% (0.05)} \) on each end. - For the left z-score, the cumulative probability is 0.05. - For the right z-score, the cumulative probability is 1 - 0.05 = 0.95. 5. **Inputting into Excel**: - Type `=NORM.S.INV(0.05)` for the left z-score. - Type `=NORM.S.INV(0.95)` for the right z-score. The results will give you the two z-scores that bound the middle 90% of the area. ### Practical Application You'll be asked to enter the z-scores you've calculated into the appropriate fields. Ensure you round your answers to two decimal places. Once you've entered your responses, submit them in ascending order for evaluation. The following screenshot demonstrates the input fields where you'll enter your z-scores: ![Z-score Input Fields](image) Here you'll find two boxes to input the z-scores separated by a space to ensure clarity and accuracy. ### Example Input: - Z-scores for the given area might be `-1.65` and `1.65`, following the rounding rule and assuming these were the calculated results. By practicing this exercise, you strengthen your statistical analysis skills and gain proficient use of Excel for complex calculations.
Transcribed Image Text:### Using Excel to Find Z-Scores for the Middle 90% of the Standard Normal Curve In this lesson, we'll use Excel to determine the z-scores that bound the middle 90% of the area under the standard normal curve. To do this, follow these steps: 1. **Understanding Z-scores**: Z-scores tell you how many standard deviations an element is from the mean. For the standard normal distribution, the mean is 0 and the standard deviation is 1. 2. **Target Area**: We need the middle 90%, which means we leave out 5% on each tail of the distribution curve. 3. **Using Excel for Calculation**: Excel has built-in functions to find these z-scores. Specifically, we will use the `NORM.S.INV` function, which returns the z-score corresponding to a given cumulative probability. 4. **Finding the Cumulative Probabilities**: - Since we need the middle 90%, we focus on the tail areas first: \( \text{5% (0.05)} \) on each end. - For the left z-score, the cumulative probability is 0.05. - For the right z-score, the cumulative probability is 1 - 0.05 = 0.95. 5. **Inputting into Excel**: - Type `=NORM.S.INV(0.05)` for the left z-score. - Type `=NORM.S.INV(0.95)` for the right z-score. The results will give you the two z-scores that bound the middle 90% of the area. ### Practical Application You'll be asked to enter the z-scores you've calculated into the appropriate fields. Ensure you round your answers to two decimal places. Once you've entered your responses, submit them in ascending order for evaluation. The following screenshot demonstrates the input fields where you'll enter your z-scores: ![Z-score Input Fields](image) Here you'll find two boxes to input the z-scores separated by a space to ensure clarity and accuracy. ### Example Input: - Z-scores for the given area might be `-1.65` and `1.65`, following the rounding rule and assuming these were the calculated results. By practicing this exercise, you strengthen your statistical analysis skills and gain proficient use of Excel for complex calculations.
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