Find the critical value z/2 that corresponds to the confidence level 87%.
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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![### Critical Value Calculation for Confidence Level
#### Problem Statement:
Find the critical value \( z_{\alpha/2} \) that corresponds to the confidence level of 87%.
#### Solution:
\[ z_{\alpha/2} = \text{[Input Box]} \]
*(Round to two decimal places as needed.)*
---
To solve this problem, you need to convert the given confidence level into a complementary probability and use a standard normal distribution table or calculator to find the critical value \( z_{\alpha/2} \).
- **Confidence Level (CL):** 87% means 0.87 probability.
- **Complementary Probability (alpha):**
\[ \alpha = 1 - 0.87 = 0.13 \]
- **Two-tailed \(\alpha\):**
\[ \alpha/2 = 0.13/2 = 0.065 \]
Now, use a standard normal distribution table or calculator to find the \( z \)-score that corresponds to the area \( 1 - 0.065 = 0.935 \) to the left of it in the standard normal distribution. This will give the critical value \( z_{\alpha/2} \).
Enter the value in the solution box, rounding to two decimal places as necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F626680b8-87a8-442c-b0ab-f04aa1b187bb%2Fda59c523-c636-4de7-9f0d-339e9a99b0a5%2Ffued78m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Critical Value Calculation for Confidence Level
#### Problem Statement:
Find the critical value \( z_{\alpha/2} \) that corresponds to the confidence level of 87%.
#### Solution:
\[ z_{\alpha/2} = \text{[Input Box]} \]
*(Round to two decimal places as needed.)*
---
To solve this problem, you need to convert the given confidence level into a complementary probability and use a standard normal distribution table or calculator to find the critical value \( z_{\alpha/2} \).
- **Confidence Level (CL):** 87% means 0.87 probability.
- **Complementary Probability (alpha):**
\[ \alpha = 1 - 0.87 = 0.13 \]
- **Two-tailed \(\alpha\):**
\[ \alpha/2 = 0.13/2 = 0.065 \]
Now, use a standard normal distribution table or calculator to find the \( z \)-score that corresponds to the area \( 1 - 0.065 = 0.935 \) to the left of it in the standard normal distribution. This will give the critical value \( z_{\alpha/2} \).
Enter the value in the solution box, rounding to two decimal places as necessary.
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