= Normal Distribution with μ P(X> 1.28) = -1.28 -1 0 μ 0 and a = 1 1.28
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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Question
![### Normal Distribution Graphs
#### C. Normal Distribution with μ = 0 and σ = 1
- **Graph Description:**
- This graph shows a standard normal distribution curve, centered at μ = 0 with a standard deviation (σ) of 1.
- The x-axis is marked with values -3, -2, -1, 0, 1, 2, 3.
- Two vertical dashed lines are drawn at x = -1.28 and x = 1.28.
- The area beyond these points (shaded in blue) represents \( P(|X| > 1.28) \).
- The left tail and right tail regions are shaded to represent this probability.
- **Annotation:**
- \( 0.1003 \)
- A note below the graph states, "That is only the area of one tail."
#### D. Normal Distribution with μ = 0 and σ = 1
- **Graph Description:**
- Another standard normal distribution curve, with the same mean and standard deviation.
- Vertical dashed lines are at x = -1.64 and x = 1.64.
- Shaded areas in the tails indicate the probability \( P(|X| > 1.64) \).
These graphs are used to demonstrate the calculation of probabilities in a standard normal distribution, focusing on the areas in the tails beyond certain z-scores. The notes clarify the meaning of the shaded regions and the calculations involved.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9d8e919-6c53-43b3-96c1-5f9438fdaf13%2F367335d2-29ba-4d84-8735-a1fcba9ac580%2Fn9vc5u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Normal Distribution Graphs
#### C. Normal Distribution with μ = 0 and σ = 1
- **Graph Description:**
- This graph shows a standard normal distribution curve, centered at μ = 0 with a standard deviation (σ) of 1.
- The x-axis is marked with values -3, -2, -1, 0, 1, 2, 3.
- Two vertical dashed lines are drawn at x = -1.28 and x = 1.28.
- The area beyond these points (shaded in blue) represents \( P(|X| > 1.28) \).
- The left tail and right tail regions are shaded to represent this probability.
- **Annotation:**
- \( 0.1003 \)
- A note below the graph states, "That is only the area of one tail."
#### D. Normal Distribution with μ = 0 and σ = 1
- **Graph Description:**
- Another standard normal distribution curve, with the same mean and standard deviation.
- Vertical dashed lines are at x = -1.64 and x = 1.64.
- Shaded areas in the tails indicate the probability \( P(|X| > 1.64) \).
These graphs are used to demonstrate the calculation of probabilities in a standard normal distribution, focusing on the areas in the tails beyond certain z-scores. The notes clarify the meaning of the shaded regions and the calculations involved.
Expert Solution
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Step 1
(c)
Find the value of P(|x|>1.28) by using MINITAB.
The value of P(|x|>1.28) is obtained by using MINITAB.
- Choose Graph > Probability Distribution Plot choose View Probability> OK.
- From Distribution, choose ‘Normal’ distribution.
- Click the Shaded Area
- Choose X Value and Both Tail for the region of the curve to shade.
- Enter the data value as 1.28.
- Click OK.
Output obtained from MINITAB is given below:
From the output, the value of P(|x|>1.28) is 0.2006 (=0.1003*2).
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