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) Z-0.44, (c) Z= 1.32, and (d) Z = 1.99

) Z-0.44, (c) Z= 1.32, and (d) Z = 1.99

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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Answer C-D
**Transcription for Educational Website:** --- ### Understanding Areas Under the Standard Normal Curve To determine the area under the standard normal curve for specific values of \( Z \), you can use the Standard Normal Distribution Table. This table provides the area (probability) to the left of a given \( Z \)-score in a standard normal distribution. #### Instructions: For each of the following \( Z \)-scores, find the area to the right: a) **\( Z = 0.99 \)** - **Area to the right:** 0.1611 b) **\( Z = 0.44 \)** - **Area to the right:** 0.33 (rounded to four decimal places as needed) c) **\( Z = 1.32 \)** - **Area to the right:** [Please calculate using the table and round to four decimal places as needed] #### Using the Standard Normal Distribution Table The displayed table, "Standard Normal Distribution Table (page 1)," shows \( Z \)-scores ranging from -3.4 to 3.4. Each row represents the first decimal place, and the columns represent the second decimal place of the \( Z \)-score. The intersection of a row and column gives the cumulative probability from the left of the distribution. To find the area to the right for a specific \( Z \)-score: 1. Locate the \( Z \)-score's value using the appropriate row and column. 2. Subtract the table value from 1 to get the area to the right. Note: A larger cumulative value indicates a greater probability to the left, meaning the area to the right will be smaller. For more precise calculations, ensure rounding is applied as necessary to achieve four decimal places. ---
Transcribed Image Text:**Transcription for Educational Website:** --- ### Understanding Areas Under the Standard Normal Curve To determine the area under the standard normal curve for specific values of \( Z \), you can use the Standard Normal Distribution Table. This table provides the area (probability) to the left of a given \( Z \)-score in a standard normal distribution. #### Instructions: For each of the following \( Z \)-scores, find the area to the right: a) **\( Z = 0.99 \)** - **Area to the right:** 0.1611 b) **\( Z = 0.44 \)** - **Area to the right:** 0.33 (rounded to four decimal places as needed) c) **\( Z = 1.32 \)** - **Area to the right:** [Please calculate using the table and round to four decimal places as needed] #### Using the Standard Normal Distribution Table The displayed table, "Standard Normal Distribution Table (page 1)," shows \( Z \)-scores ranging from -3.4 to 3.4. Each row represents the first decimal place, and the columns represent the second decimal place of the \( Z \)-score. The intersection of a row and column gives the cumulative probability from the left of the distribution. To find the area to the right for a specific \( Z \)-score: 1. Locate the \( Z \)-score's value using the appropriate row and column. 2. Subtract the table value from 1 to get the area to the right. Note: A larger cumulative value indicates a greater probability to the left, meaning the area to the right will be smaller. For more precise calculations, ensure rounding is applied as necessary to achieve four decimal places. ---
### Educational Exercise: Calculating Areas Under the Standard Normal Curve This exercise involves determining the area under the standard normal curve for specific Z-values using a standard normal distribution table. #### Tasks and Solutions 1. **Determine the area to the right of Z = 0.99:** - The area to the right of Z = 0.99 is **0.1611**. - This area is represented as a probability, rounded to four decimal places. 2. **Determine the area to the right of Z = -0.44:** - The area to the right of Z = -0.44 is **0.33**. - Remember to round the number to four decimal places as required. 3. **Determine the area to the right of Z = 1.32:** - The area to the right of Z = 1.32 is **0.0934**. - Ensure rounding to four decimal places. #### Understanding the Standard Normal Distribution Table **Standard Normal Distribution Table (Page 2):** - The table shown is a section of a standard normal distribution table, which lists cumulative probabilities related to the standard normal distribution (mean = 0, standard deviation = 1). - **Rows and Columns:** - The leftmost column represents the integer and first decimal of the Z-value (e.g., 0.0, 0.1, ..., 2.9). - The top row represents the second decimal place (e.g., 0.00, 0.01, ..., 0.09). - The intersection of a row and column gives you the cumulative probability from the mean to that specific Z-value. - **Finding Values:** - To find a Z-value's cumulative probability up to that point, locate the Z-value by combining the row and column. This probability represents the area under the curve to the left of that Z-value. For calculations involving areas to the right, subtract the table value from 1, as the table provides the cumulative area from the left. This exercise will enhance your comprehension of how to utilize a standard normal distribution table to find areas under the curve, a fundamental skill in statistics.
Transcribed Image Text:### Educational Exercise: Calculating Areas Under the Standard Normal Curve This exercise involves determining the area under the standard normal curve for specific Z-values using a standard normal distribution table. #### Tasks and Solutions 1. **Determine the area to the right of Z = 0.99:** - The area to the right of Z = 0.99 is **0.1611**. - This area is represented as a probability, rounded to four decimal places. 2. **Determine the area to the right of Z = -0.44:** - The area to the right of Z = -0.44 is **0.33**. - Remember to round the number to four decimal places as required. 3. **Determine the area to the right of Z = 1.32:** - The area to the right of Z = 1.32 is **0.0934**. - Ensure rounding to four decimal places. #### Understanding the Standard Normal Distribution Table **Standard Normal Distribution Table (Page 2):** - The table shown is a section of a standard normal distribution table, which lists cumulative probabilities related to the standard normal distribution (mean = 0, standard deviation = 1). - **Rows and Columns:** - The leftmost column represents the integer and first decimal of the Z-value (e.g., 0.0, 0.1, ..., 2.9). - The top row represents the second decimal place (e.g., 0.00, 0.01, ..., 0.09). - The intersection of a row and column gives you the cumulative probability from the mean to that specific Z-value. - **Finding Values:** - To find a Z-value's cumulative probability up to that point, locate the Z-value by combining the row and column. This probability represents the area under the curve to the left of that Z-value. For calculations involving areas to the right, subtract the table value from 1, as the table provides the cumulative area from the left. This exercise will enhance your comprehension of how to utilize a standard normal distribution table to find areas under the curve, a fundamental skill in statistics.
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