**Transcription for Educational Website**---**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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Answered: 3) Find the shaded region, if z = .19

Math

Statistics

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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**Transcription for Educational Website**

---

**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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