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.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2f53b00-06a8-498f-8336-39884f19308e%2Fa81554d8-59a3-4ad6-8420-d325b56d4e85%2Fxwxgnm_processed.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)