Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. z= -0.88 z-1.21 The area of the shaded region is
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. z= -0.88 z-1.21 The area of the shaded region is
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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
Transcribed Image Text:**Finding the Area of the Shaded Region in a Standard Normal Distribution**
In this lesson, we will determine the area of the shaded region in a standard normal distribution graph. The graph in question illustrates the standard normal distribution of bone density scores, which follows a distribution with a mean (μ) of 0 and a standard deviation (σ) of 1.
**Graph Description:**
To the right of the text, a standard normal distribution curve (also known as a bell curve) is shown. The curve is symmetrical, centered at the mean value of 0. The shaded region under the curve represents the area we are interested in finding.
**Notable Points on the Graph:**
- The z-scores (representing the number of standard deviations away from the mean) for the limits of the shaded region are indicated.
- The left boundary of the shaded region corresponds to \( z = -0.88 \).
- The right boundary of the shaded region corresponds to \( z = 1.21 \).
**Objective:**
- Calculate the area of the shaded region between these z-scores.
**Instructions:**
1. **Identify Z-Scores**: Determine the z-scores that mark the boundaries of the shaded region: \( z = -0.88 \) and \( z = 1.21 \).
2. **Look Up Values**: Use the standard normal (Z) table or a calculator to find the area under the curve to the left of each z-score.
3. **Calculate Area**:
- Find the area to the left of \( z = -0.88 \).
- Find the area to the left of \( z = 1.21 \).
- Subtract the area corresponding to \( z = -0.88 \) from the area corresponding to \( z = 1.21 \) to find the area of the shaded region.
4. **Round**: Present the area rounded to four decimal places.
**Question:**
- What is the area of the shaded region? Please round your answer to four decimal places.
By following these steps, we can determine the area under the curve between the specified z-scores, effectively quantifying the likelihood of bone density scores falling within this range.
Insert your answer in the blank provided after computation.
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