What is the probability of obtaining a Z score above +2.5
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
Transcribed Image Text:**Exercise on Normal Distribution**
*Instructions: Be sure to show your work for all the following questions and assume a normal distribution.*
**Question:**
What is the probability of obtaining a Z score above +2.5?
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**Explanation:**
To solve this question, you need to understand the properties of the standard normal distribution, where the mean is 0 and the standard deviation is 1.
1. **Identify the Z Score:**
- A Z score of +2.5 indicates that the score is 2.5 standard deviations above the mean.
2. **Use the Standard Normal Distribution Table:**
- Look up the Z score of 2.5 in the standard normal distribution table to find the area to the left of the Z score. This will give you the probability of a score being below +2.5.
3. **Calculate the Probability:**
- To find the probability of a Z score being above +2.5, subtract the table value from 1. This is because the total area under the normal distribution curve is 1.
4. **Conclusion:**
- The probability calculated will be the percentage of data points that lie above a Z score of +2.5 in a normally distributed dataset.
In doing your calculations, make sure to show your work clearly, indicating each step for full comprehension.
Expert Solution
Step 1
We have to find the probability of obtaining a Z score above +2.5. Here we assume normal distribution. So, in this problem, .
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