Find the z-scores for which 15% of the distribution's area lies between −z and z. The image displays a segment of a Standard Normal Distribution Table, commonly used in statistics to find the probability of a statistic lying below a given Z-score in a standard normal distribution.**Table Explanation:**- **Rows and Columns:** - The first column represents Z-scores ranging from -3.4 to -1.3 in increments of 0.1. - The top row, labeled with decimal values (0.00 to 0.09), represents the hundredths place of the Z-score.- **Values in the Table:** - Each cell in the table contains the cumulative probability (to four decimal places) for the corresponding Z-score. - To find the cumulative probability for a specific Z-score, combine the row and column. For example, for Z = -2.5 and an additional 0.07, locate the row -2.5 and column 0.07, which yields a cumulative probability of 0.0069.**Usage:**This table aids in determining the probability that a score is below a certain Z-score in a normal distribution. It is essential for statistical analyses, especially in hypothesis testing and confidence interval calculations. Below is the transcription of the Z-table, commonly used in statistics to find the probability of a standard normal distribution:```z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.68790.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.72240.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422

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Find the z-scores for which 15% of the distribution's area lies between −z and z.

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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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

Find the z-scores for which 15% of the distribution's area lies between −z and z.

The image displays a segment of a Standard Normal Distribution Table, commonly used in statistics to find the probability of a statistic lying below a given Z-score in a standard normal distribution.

**Table Explanation:**

- **Rows and Columns:**
- The first column represents Z-scores ranging from -3.4 to -1.3 in increments of 0.1.
- The top row, labeled with decimal values (0.00 to 0.09), represents the hundredths place of the Z-score.

- **Values in the Table:**
- Each cell in the table contains the cumulative probability (to four decimal places) for the corresponding Z-score.
- To find the cumulative probability for a specific Z-score, combine the row and column. For example, for Z = -2.5 and an additional 0.07, locate the row -2.5 and column 0.07, which yields a cumulative probability of 0.0069.

**Usage:**
This table aids in determining the probability that a score is below a certain Z-score in a normal distribution. It is essential for statistical analyses, especially in hypothesis testing and confidence interval calculations.

Below is the transcription of the Z-table, commonly used in statistics to find the probability of a standard normal distribution:

```
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422

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