use the table !Zuckerman (1994) developed a standardized scale to measure sensation seeking personality based on 4 traits: adventure seeking, experience seeking, disinhibition and boredom susceptibility. The following table identifies each trait being measured, summarizes its characteristics, and provides the participant’ score on it. Assume that the possible scores on each test are normally distributed. TraitμσParticipant’s ScoreAdventure Seeking7.342.296.50Experience Seeking4.721.755.75Disinhibition6.452.334.25Boredom Susceptibility3.641.056.13 Change each of the participant’s score to its z-score equivalentOn which trait did the participant score in the highest position?On which trait did the participant score in the lowest position?What is the percentile rank of the participant’s Adventure Seeking trait?What percentage of the participants with the Disinhibition trait score higher than the participant?Between what two scores on Boredom Susceptibility did the middle 95% of the participants lie?What percent of the participants had scores between X = 2 and X = 8 on Adventure Seeking trait? The image displays data from a statistical table focused on the standard normal distribution. Let's break down the table columns and their meanings for a better understanding.### Table Format:The table is organized into four main columns, repeated for two sets, using these headers:1. **(A) Proportion in Body**: This column lists the cumulative proportion of the standard normal distribution or the probability of occurrence from the mean up to the given z-value. 2. **(B) Proportion in Tail**: This column shows the proportion or probability in the tail beyond the given z-value.3. **(C) Proportion Between Mean and z**: This reflects the probability of occurrence or the proportion between the mean (0) and the specified z-value.4. **(D) z**: This represents the z-value, a point on the standard normal distribution, which corresponds to the probabilities listed in the other columns.### Explanation of Values:- The table provides precise decimal values for each z-value starting from 0.50 and advancing by increments of 0.01 up to 1.49. - For instance, a z-value of 0.50 has: - Proportion in Body: 0.6915 - Proportion in Tail: 0.3085 - Proportion Between Mean and z: 0.1915- As the z-value increases, the proportion in the body increases while the proportion in the tail decreases.### Usage:This statistical table is typically used in statistics to determine probabilities and percentiles for standard normal distributions. It's essential for hypothesis testing, constructing confidence intervals, and various statistical analyses.This kind of table is found in educational resources aimed at teaching statistics, probability theory, and data analysis. ### Appendix B: Statistical Tables#### Table B.1: The Unit Normal TableThis table provides key information about the standard normal distribution and its corresponding z-scores.**Explanations:**- **Column A** lists z-score values. A vertical line drawn through a normal distribution at a specific z-score divides the distribution into two sections.- **Column B** identifies the proportion in the larger section, called the body.- **Column C** identifies the proportion in the smaller section, called the tail.- **Column D** identifies the proportion between the mean and the specified z-score.**Note:** The properties of a normal distribution are symmetrical, meaning the proportions for negative z-scores are the same as for positive z-scores.#### Diagrams:1. **First Diagram:** - Illustrates the normal distribution curve with a vertical line at a positive z-score. - The larger area, labeled "Body" (B), represents the proportion of data points in this section. - The smaller area, labeled "Tail" (C), represents the remaining proportion. 2. **Second Diagram:** - Similar illustration with a line at a negative z-score. - Also shows the "Body" (B) and "Tail" (C) regions. 3. **Third Diagram:** - Demonstrates the area between the mean and a z-score, labeled (D).#### Table Data Overview:The table presents z-score values (A) from 0.00 to 0.49, their corresponding proportions in the body (B), in the tail (C), and between the mean and z (D).For example:- A z-score of 0.00 has a body proportion of .5000, a tail proportion of .5000, and a mean to z proportion of .0000.- A z-score of 0.25 has a body proportion of .5987, a tail proportion of .4013, and a mean to z proportion of .0987.This table is crucial for statistical calculations involving standard normal distributions.

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Answered: Change each of the participant’s score…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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use the table !

Zuckerman (1994) developed a standardized scale to measure sensation seeking personality based on 4 traits: adventure seeking, experience seeking, disinhibition and boredom susceptibility. The following table identifies each trait being measured, summarizes its characteristics, and provides the participant’ score on it. Assume that the possible scores on each test are normally distributed.

Trait	μ	σ	Participant’s Score
Adventure Seeking	7.34	2.29	6.50
Experience Seeking	4.72	1.75	5.75
Disinhibition	6.45	2.33	4.25
Boredom Susceptibility	3.64	1.05	6.13

Change each of the participant’s score to its z-score equivalent
On which trait did the participant score in the highest position?
On which trait did the participant score in the lowest position?
What is the percentile rank of the participant’s Adventure Seeking trait?
What percentage of the participants with the Disinhibition trait score higher than the participant?
Between what two scores on Boredom Susceptibility did the middle 95% of the participants lie?
What percent of the participants had scores between X = 2 and X = 8 on Adventure Seeking trait?

The image displays data from a statistical table focused on the standard normal distribution. Let's break down the table columns and their meanings for a better understanding.

### Table Format:

The table is organized into four main columns, repeated for two sets, using these headers:

1. **(A) Proportion in Body**: This column lists the cumulative proportion of the standard normal distribution or the probability of occurrence from the mean up to the given z-value.

2. **(B) Proportion in Tail**: This column shows the proportion or probability in the tail beyond the given z-value.

3. **(C) Proportion Between Mean and z**: This reflects the probability of occurrence or the proportion between the mean (0) and the specified z-value.

4. **(D) z**: This represents the z-value, a point on the standard normal distribution, which corresponds to the probabilities listed in the other columns.

### Explanation of Values:

- The table provides precise decimal values for each z-value starting from 0.50 and advancing by increments of 0.01 up to 1.49.

- For instance, a z-value of 0.50 has:
- Proportion in Body: 0.6915
- Proportion in Tail: 0.3085
- Proportion Between Mean and z: 0.1915

- As the z-value increases, the proportion in the body increases while the proportion in the tail decreases.

### Usage:

This statistical table is typically used in statistics to determine probabilities and percentiles for standard normal distributions. It's essential for hypothesis testing, constructing confidence intervals, and various statistical analyses.

This kind of table is found in educational resources aimed at teaching statistics, probability theory, and data analysis.

### Appendix B: Statistical Tables

#### Table B.1: The Unit Normal Table

This table provides key information about the standard normal distribution and its corresponding z-scores.

**Explanations:**

- **Column A** lists z-score values. A vertical line drawn through a normal distribution at a specific z-score divides the distribution into two sections.
- **Column B** identifies the proportion in the larger section, called the body.
- **Column C** identifies the proportion in the smaller section, called the tail.
- **Column D** identifies the proportion between the mean and the specified z-score.

**Note:** The properties of a normal distribution are symmetrical, meaning the proportions for negative z-scores are the same as for positive z-scores.

#### Diagrams:

1. **First Diagram:**
- Illustrates the normal distribution curve with a vertical line at a positive z-score.
- The larger area, labeled "Body" (B), represents the proportion of data points in this section.
- The smaller area, labeled "Tail" (C), represents the remaining proportion.

2. **Second Diagram:**
- Similar illustration with a line at a negative z-score.
- Also shows the "Body" (B) and "Tail" (C) regions.

3. **Third Diagram:**
- Demonstrates the area between the mean and a z-score, labeled (D).

#### Table Data Overview:

The table presents z-score values (A) from 0.00 to 0.49, their corresponding proportions in the body (B), in the tail (C), and between the mean and z (D).

For example:
- A z-score of 0.00 has a body proportion of .5000, a tail proportion of .5000, and a mean to z proportion of .0000.
- A z-score of 0.25 has a body proportion of .5987, a tail proportion of .4013, and a mean to z proportion of .0987.

This table is crucial for statistical calculations involving standard normal distributions.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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