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(a) The area to the right of Z=0.99 is (Round to four decimal places as needed.).

(a) The area to the right of Z=0.99 is (Round to four decimal places as needed.).

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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**Title: Understanding the Standard Normal Distribution Table** **Section 1: Problem Statement** Determine the area under the standard normal curve that lies to the right of: - (a) \( Z = 0.99 \), - (b) \( Z = -0.44 \), - (c) \( Z = 1.32 \), - (d) \( Z = 1.99 \). **Instructions:** Round to four decimal places as needed. **Section 2: Resources** Click here to view the standard normal distribution table [page 1]. Click here to view the standard normal distribution table [page 2]. **Section 3: Explanation of the Diagram** The image includes a screenshot of the "Standard Normal Distribution Table" (page 1), which provides probabilities associated with specific Z-scores in a standard normal distribution. The table is essential for finding the cumulative probability corresponding to a given Z-score. - **Illustration:** At the top of the table, a bell curve is provided, demonstrating the standard normal distribution, with the shaded area representing the probability. - **Table Layout:** The table is structured in rows and columns: - The leftmost column lists Z-scores from -3.4 to -1.4 in increments of 0.1. - The top row lists additional decimal points from 0.00 to 0.09 to fine-tune these Z-scores. - The intersection of the row and column gives the probability to the left of the Z-score under the standard normal curve. - **Usage:** To find the probability to the right of a Z-score, locate the score in the table and subtract the corresponding probability from 1. **Section 4: Using the Table** For practical application: - To find the area to the right of \( Z = 0.99 \), identify the row for \( Z = 0.9 \) and then the column for 0.09. Subtract the table value from 1. - Repeat the process for other given Z-scores. This exercise aids in understanding the application of Z-scores and the use of the standard normal distribution table in statistical analysis.
Transcribed Image Text:**Title: Understanding the Standard Normal Distribution Table** **Section 1: Problem Statement** Determine the area under the standard normal curve that lies to the right of: - (a) \( Z = 0.99 \), - (b) \( Z = -0.44 \), - (c) \( Z = 1.32 \), - (d) \( Z = 1.99 \). **Instructions:** Round to four decimal places as needed. **Section 2: Resources** Click here to view the standard normal distribution table [page 1]. Click here to view the standard normal distribution table [page 2]. **Section 3: Explanation of the Diagram** The image includes a screenshot of the "Standard Normal Distribution Table" (page 1), which provides probabilities associated with specific Z-scores in a standard normal distribution. The table is essential for finding the cumulative probability corresponding to a given Z-score. - **Illustration:** At the top of the table, a bell curve is provided, demonstrating the standard normal distribution, with the shaded area representing the probability. - **Table Layout:** The table is structured in rows and columns: - The leftmost column lists Z-scores from -3.4 to -1.4 in increments of 0.1. - The top row lists additional decimal points from 0.00 to 0.09 to fine-tune these Z-scores. - The intersection of the row and column gives the probability to the left of the Z-score under the standard normal curve. - **Usage:** To find the probability to the right of a Z-score, locate the score in the table and subtract the corresponding probability from 1. **Section 4: Using the Table** For practical application: - To find the area to the right of \( Z = 0.99 \), identify the row for \( Z = 0.9 \) and then the column for 0.09. Subtract the table value from 1. - Repeat the process for other given Z-scores. This exercise aids in understanding the application of Z-scores and the use of the standard normal distribution table in statistical analysis.
The image displays a Standard Normal Distribution Table, which is used in statistics to find the probability associated with a standard normal random variable Z. This table is specifically useful for determining the area under the normal curve to the left of a given Z-score. ### How to Read the Table: 1. **Z-Score**: The value in the leftmost column indicates the Z-score to the first decimal point. 2. **Top Row**: This row indicates the second decimal place of the Z-score. 3. **Intersection Values**: To find the probability, locate the Z-score's first decimal on the left column, then move across the row to the column corresponding to the Z-score's second decimal. The value at this intersection is the area under the curve to the left of the Z-score. ### Explanation: - The table values represent the cumulative probability from the extreme left of the distribution (Z = -∞) to a particular Z-score. - For example, to find the probability for Z = -1.23, find -1.2 on the left column, and then move to the right to the 0.03 column. The value at this intersection is approximately 0.1093, meaning there is a 10.93% chance that a standard normal random variable is less than -1.23. Understanding how to use this table allows for the computation of probabilities and is essential for statistical analysis in fields such as psychology, business, and natural sciences.
Transcribed Image Text:The image displays a Standard Normal Distribution Table, which is used in statistics to find the probability associated with a standard normal random variable Z. This table is specifically useful for determining the area under the normal curve to the left of a given Z-score. ### How to Read the Table: 1. **Z-Score**: The value in the leftmost column indicates the Z-score to the first decimal point. 2. **Top Row**: This row indicates the second decimal place of the Z-score. 3. **Intersection Values**: To find the probability, locate the Z-score's first decimal on the left column, then move across the row to the column corresponding to the Z-score's second decimal. The value at this intersection is the area under the curve to the left of the Z-score. ### Explanation: - The table values represent the cumulative probability from the extreme left of the distribution (Z = -∞) to a particular Z-score. - For example, to find the probability for Z = -1.23, find -1.2 on the left column, and then move to the right to the 0.03 column. The value at this intersection is approximately 0.1093, meaning there is a 10.93% chance that a standard normal random variable is less than -1.23. Understanding how to use this table allows for the computation of probabilities and is essential for statistical analysis in fields such as psychology, business, and natural sciences.
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