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Determine the value of C P(-0.82 ≤ z = C) = 0.7810

Determine the value of C P(-0.82 ≤ z = C) = 0.7810

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 problem: \[ P(-0.82 \leq z \leq C) = 0.7810 \] In this scenario, we are asked to find the value of \( C \) for which the probability that the z-score \( z \) lies between -0.82 and \( C \) equals 0.7810. To solve this problem: 1. **Understanding the Probability and z-Scores:** - The probability \( P(-0.82 \leq z \leq C) = 0.7810 \) signifies that the area under the standard normal curve between \( z = -0.82 \) and \( z = C \) is 0.7810. 2. **Using Standard Normal Distribution Tables or a z-Score Calculator:** - First, we determine the cumulative probability associated with \( z = -0.82 \). - Next, we add 0.7810 to this probability to determine the cumulative probability corresponding to \( z = C \). - Finally, we find the z-score corresponding to this cumulative probability. This problem is a typical example in statistics where we need to locate a specific z-score corresponding to a given probability, utilizing the standard normal distribution table or statistical software for accurate results. Below provided is the handwritten transcription of the problem: **Problem Statement:** \[ \text{Determine the value of } C \] \[ P(-0.82 \leq z \leq C) = 0.7810 \]
Transcribed Image Text:### Determine the Value of C Given the problem: \[ P(-0.82 \leq z \leq C) = 0.7810 \] In this scenario, we are asked to find the value of \( C \) for which the probability that the z-score \( z \) lies between -0.82 and \( C \) equals 0.7810. To solve this problem: 1. **Understanding the Probability and z-Scores:** - The probability \( P(-0.82 \leq z \leq C) = 0.7810 \) signifies that the area under the standard normal curve between \( z = -0.82 \) and \( z = C \) is 0.7810. 2. **Using Standard Normal Distribution Tables or a z-Score Calculator:** - First, we determine the cumulative probability associated with \( z = -0.82 \). - Next, we add 0.7810 to this probability to determine the cumulative probability corresponding to \( z = C \). - Finally, we find the z-score corresponding to this cumulative probability. This problem is a typical example in statistics where we need to locate a specific z-score corresponding to a given probability, utilizing the standard normal distribution table or statistical software for accurate results. Below provided is the handwritten transcription of the problem: **Problem Statement:** \[ \text{Determine the value of } C \] \[ P(-0.82 \leq z \leq C) = 0.7810 \]
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