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Determine the value of C P(1.06 ≤ Z ≤. C) = 0.1299

Determine the value of C P(1.06 ≤ Z ≤. C) = 0.1299

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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**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 \( C \).
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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