MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Standard Normal Distribution and Shaded Area Calculation

#### Problem Statement:
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

- **Graph Description:**
  - The graph shows a bell curve representing the standard normal distribution.
  - A vertical line marks a point on the horizontal axis labeled \( z = 0.53 \).
  - The region to the left of this line under the curve is shaded.

#### Links to Table:
- [Click to view page 1 of the table.](#)
- [Click to view page 2 of the table.](#)

#### Instructions:
Calculate the area of the shaded region using the standard normal distribution table provided through the links. Ensure you round your answer to four decimal places as needed.

**Answer Box:**
- The area of the shaded region is _____. 

**Note:** You have a time limit of 2 hours, 52 minutes, and 5 seconds to complete this calculation.

---

This exercise helps students practice finding probabilities using the standard normal distribution and interpreting z-scores with the help of tables. The use of graphical representation aids in visualizing the concept of area under the curve corresponding to a specific z-value.
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Transcribed Image Text:### Standard Normal Distribution and Shaded Area Calculation #### Problem Statement: Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. - **Graph Description:** - The graph shows a bell curve representing the standard normal distribution. - A vertical line marks a point on the horizontal axis labeled \( z = 0.53 \). - The region to the left of this line under the curve is shaded. #### Links to Table: - [Click to view page 1 of the table.](#) - [Click to view page 2 of the table.](#) #### Instructions: Calculate the area of the shaded region using the standard normal distribution table provided through the links. Ensure you round your answer to four decimal places as needed. **Answer Box:** - The area of the shaded region is _____. **Note:** You have a time limit of 2 hours, 52 minutes, and 5 seconds to complete this calculation. --- This exercise helps students practice finding probabilities using the standard normal distribution and interpreting z-scores with the help of tables. The use of graphical representation aids in visualizing the concept of area under the curve corresponding to a specific z-value.
**Standard Normal Distribution Table (Page 2)**

This table provides cumulative probabilities for the standard normal distribution, which is a continuous probability distribution. The rows represent the z-score up to one decimal place, and the columns add the second decimal place for the z-score. The values inside the table are the cumulative probabilities P(Z ≤ z).

For example, to find the cumulative probability for a z-score of 0.47:
1. Locate the row for 0.4.
2. Move along this row to the column for 0.07.
3. The intersecting cell shows a value of 0.6808, which means the cumulative probability P(Z ≤ 0.47) is 0.6808.

The table is generally used to find probabilities and percentiles associated with the normal distribution. Understanding how to read this table is essential for statistical analysis and hypothesis testing in various fields, such as psychology, business, and engineering.
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Transcribed Image Text:**Standard Normal Distribution Table (Page 2)** This table provides cumulative probabilities for the standard normal distribution, which is a continuous probability distribution. The rows represent the z-score up to one decimal place, and the columns add the second decimal place for the z-score. The values inside the table are the cumulative probabilities P(Z ≤ z). For example, to find the cumulative probability for a z-score of 0.47: 1. Locate the row for 0.4. 2. Move along this row to the column for 0.07. 3. The intersecting cell shows a value of 0.6808, which means the cumulative probability P(Z ≤ 0.47) is 0.6808. The table is generally used to find probabilities and percentiles associated with the normal distribution. Understanding how to read this table is essential for statistical analysis and hypothesis testing in various fields, such as psychology, business, and engineering.
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