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= Normal Distribution with μ P(X> 1.28) = -1.28 -1 0 μ 0 and a = 1 1.28

= Normal Distribution with μ P(X> 1.28) = -1.28 -1 0 μ 0 and a = 1 1.28

MATLAB: An Introduction with Applications
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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### 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.
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
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.

  1. Choose Graph > Probability Distribution Plot choose View Probability> OK.
  2. From Distribution, choose ‘Normal’ distribution.
  3. Click the Shaded Area
  4. Choose X Value and Both Tail for the region of the curve to shade.
  5. Enter the data value as 1.28.
  6. Click OK.

Output obtained from MINITAB is given below:

Statistics homework question answer, step 1, image 1

From the output, the value of P(|x|>1.28) is 0.2006 (=0.1003*2).

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