K Find the res that Click the icon to view a table of areas under the normal curve. The Z-scores are (Use a comma to separate answers as needed. Round to two decimal places as needed.) Tables of Areas under the Area Z .00 .01 0.0003 0.0003 -3.4 -3.3 0.0005 0.0005 -3.2 0.0007 0.0007 0.0010 0.0009 -3.1 -3.0 0.0013 0.0013 T 00010 00018
K Find the res that Click the icon to view a table of areas under the normal curve. The Z-scores are (Use a comma to separate answers as needed. Round to two decimal places as needed.) Tables of Areas under the Area Z .00 .01 0.0003 0.0003 -3.4 -3.3 0.0005 0.0005 -3.2 0.0007 0.0007 0.0010 0.0009 -3.1 -3.0 0.0013 0.0013 T 00010 00018
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:**Educational Website Content: Understanding Z-Scores and the Standard Normal Distribution**
To determine the Z-scores that separate the middle 70% of the distribution from the tails in a standard normal distribution, you'll need to consult a Z-table, which provides the areas (probabilities) associated with standard normal Z-scores.
### Instruction:
1. **Task Explanation:**
- Find the Z-scores that separate the middle 70% of the distribution from the area in the tails of the standard normal distribution.
2. **How to Access the Table:**
- Click on the icon to view a table of areas under the normal curve.
3. **Input Prompt:**
- Enter the Z-scores in the input box. Use a comma to separate multiple answers, and round each value to two decimal places as needed.
### Z-Table Overview:
The displayed table, titled "Tables of Areas under the Normal Curve," is a comprehensive chart listing the cumulative probabilities associated with different Z-scores under a standard normal distribution. The table is organized into columns, each labeled with a decimal ranging from .00 to .09. The rows correspond to Z-score values ranging from negative to positive.
**Diagram Explanation:**
- The small diagram shows a bell-shaped curve, typical of a normal distribution. The shaded region under the curve indicates the area referred to by the table data, which corresponds to cumulative probabilities.
**How to Use the Table:**
- To find the area (probability) corresponding to a specific Z-score, locate the Z-score value on the left column. Move horizontally across the row to find the specific decimal place column that matches your Z-score.
- The intersection of the row and column will give you the cumulative probability that corresponds to that Z-score.
**Finding the Z-Scores for the Middle 70%:**
- To find the Z-scores separating the middle 70% of the distribution, you should aim for cumulative probabilities of 0.15 (tail) and 0.85 (opposite tail), since the tails outside the middle 70% are split evenly.
- Using the Z-table, find the values of Z that correspond to these cumulative probabilities. Enter these Z-scores into the input box.
This fundamental tool in statistics allows you to apply Z-scores in analyzing data and calculating probabilities under the curve.
**Interactive Elements:**
- Buttons labeled "Print" and "Done" allow users to print the page or complete the activity
Transcribed Image Text:The image is a table titled "Tables of Areas under the Normal Curve." It is a standard normal distribution table used to find the area (or probability) to the left of a given z-score.
### Explanation of the Table:
- **Rows and Columns**: The table is organized with z-scores listed along the leftmost column, and additional decimal places across the top row.
- **Z-Score**: Each value in the leftmost column represents the z-score up to the first decimal place (e.g., -3.4, -2.3, 0.5, etc.).
- **Additional Decimal Places**: The values along the top row represent the second decimal place of the z-score (e.g., .00, .01, .02, etc.).
- **Probability Values**: The intersection of a row and column gives the cumulative probability from the mean to a z-score. For example, to find the area under the curve for a z-score of 0.56, locate 0.5 in the leftmost column and 0.06 in the top row to find the corresponding value in the table.
- **Color Coding**: The table features alternating color bands for easy reading, though specific colors or patterns are not detailed.
This table helps calculate probabilities related to the standard normal distribution by giving the cumulative probability from the mean to any given z-score.
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