Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Click to view page 1 of the table. Click to view page 2 of the table. 70 115 The area of the shaded region is 0.8185 . (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Understanding the Area of the Shaded Region in a Normal Distribution**

In this exercise, we are tasked with finding the area of a shaded region within a normal distribution curve, which represents IQ scores of adults. These IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

**Diagram Description:**

To the right, there is a bell-shaped curve (characteristic of a normal distribution) that is shaded between the IQ scores of 70 and 115. This shading visually represents the portion of the data within these IQ scores.

**Details and Calculations:**

- **Mean (μ):** 100
- **Standard Deviation (σ):** 15
- **Shaded Region range:** IQ scores from 70 to 115

**Result:**

The calculated area of the shaded region is **0.8185**, rounded to four decimal places. This area represents the probability or proportion of the adult population with IQ scores between 70 and 115.

**Using Tables:**

For further calculations, refer to detailed statistical tables:
- [Page 1 of the Statistical Table](#)
- [Page 2 of the Statistical Table](#)

The graphical representation and the associated calculations are crucial for understanding the distribution and occurrence of specific IQ scores within a given population.

**Interactive Element:**

Below the graph is an input box where users can enter answers to related problems, encouraging further engagement with the content.
Transcribed Image Text:**Understanding the Area of the Shaded Region in a Normal Distribution** In this exercise, we are tasked with finding the area of a shaded region within a normal distribution curve, which represents IQ scores of adults. These IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. **Diagram Description:** To the right, there is a bell-shaped curve (characteristic of a normal distribution) that is shaded between the IQ scores of 70 and 115. This shading visually represents the portion of the data within these IQ scores. **Details and Calculations:** - **Mean (μ):** 100 - **Standard Deviation (σ):** 15 - **Shaded Region range:** IQ scores from 70 to 115 **Result:** The calculated area of the shaded region is **0.8185**, rounded to four decimal places. This area represents the probability or proportion of the adult population with IQ scores between 70 and 115. **Using Tables:** For further calculations, refer to detailed statistical tables: - [Page 1 of the Statistical Table](#) - [Page 2 of the Statistical Table](#) The graphical representation and the associated calculations are crucial for understanding the distribution and occurrence of specific IQ scores within a given population. **Interactive Element:** Below the graph is an input box where users can enter answers to related problems, encouraging further engagement with the content.
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