Determine the value of C P(1.06 ≤ Z ≤. C) = 0.1299
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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![**Determine the Value of C**
Given the probability equation:
\[ P(1.06 \leq Z \leq C) = 0.1299 \]
To solve this problem:
1. **Identify the Range of Z-scores:**
- The lower limit of the Z-score is 1.06.
- The upper limit of the Z-score is denoted by \( C \).
2. **Probability Requirement:**
- The area under the normal curve between the Z-scores \( 1.06 \) and \( C \) is equal to \( 0.1299 \).
**Steps:**
1. **Find the cumulative probability for the lower Z-score (1.06):**
- Use the standard normal distribution table or a calculator to find the cumulative probability \( P(Z \leq 1.06) \).
2. **Determine the cumulative probability for the range:**
- Since the cumulative probability for \( 1.06 \leq Z \leq C \) is given as \( 0.1299 \), add this value to the cumulative probability found in step 1.
3. **Find the corresponding Z-score (C):**
- Use the standard normal distribution table or a calculator to find the Z-score that corresponds to the cumulative probability obtained in step 2.
By following these steps, you can determine the exact value of \( C \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2561c632-65dd-4d60-9cc7-c4695e3617a7%2F15fbbb0d-4352-491c-ab1a-b8255814fd23%2Ftbaeaob_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine the Value of C**
Given the probability equation:
\[ P(1.06 \leq Z \leq C) = 0.1299 \]
To solve this problem:
1. **Identify the Range of Z-scores:**
- The lower limit of the Z-score is 1.06.
- The upper limit of the Z-score is denoted by \( C \).
2. **Probability Requirement:**
- The area under the normal curve between the Z-scores \( 1.06 \) and \( C \) is equal to \( 0.1299 \).
**Steps:**
1. **Find the cumulative probability for the lower Z-score (1.06):**
- Use the standard normal distribution table or a calculator to find the cumulative probability \( P(Z \leq 1.06) \).
2. **Determine the cumulative probability for the range:**
- Since the cumulative probability for \( 1.06 \leq Z \leq C \) is given as \( 0.1299 \), add this value to the cumulative probability found in step 1.
3. **Find the corresponding Z-score (C):**
- Use the standard normal distribution table or a calculator to find the Z-score that corresponds to the cumulative probability obtained in step 2.
By following these steps, you can determine the exact value of \( C \).
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