3) Find the shaded region, if z = .19
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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**Exercise 3: Finding the Shaded Region**
Given a standard normal distribution curve, find the area of the shaded region, if \( z = 0.19 \).
**Graph Description:**
- The diagram depicts a standard normal distribution curve with a bell shape.
- The portion of the curve to the left of the line at \( z = 0.19 \) is shaded in blue.
- The vertical line at \( z = 0.19 \) marks the boundary of the shaded region on the curve.
The task is to calculate the area of the shaded region, which represents the probability that a random variable \( Z \) is less than or equal to 0.19 in the standard normal distribution.
**Steps to Solve:**
1. **Use the Standard Normal Distribution Table:**
- Locate the value of \( z = 0.19 \) in the Z-table to find the corresponding probability.
2. **Interpret the Result:**
- The table provides the cumulative probability for the shaded area to the left of \( z = 0.19 \).
3. **Check with Technology:**
- Alternatively, use statistical software or a calculator that has standard normal distribution functions for quick computations.
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