Determine the value of C P(-1.05 ≤ Z≤ 0) = 0.8392 PO
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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![### Determining the Value of \(c\)
In this exercise, we aim to determine the value of \(c\) given the following probability statement:
\[P(-1.05 \leq Z \leq c) = 0.8392\]
This problem involves finding the value of \(c\) in a standard normal distribution (Z-distribution) that satisfies the given probability.
- **Z** refers to the standard normal random variable.
- **P** denotes probability.
- \([-1.05 \leq Z \leq c]\) represents the range of Z-scores we are interested in.
- \(0.8392\) is the cumulative probability for that range.
#### Step-by-Step Solution
To solve this, follow these steps:
1. **Understand the Problem**: The given information tells us that the probability that Z lies between -1.05 and \(c\) is 0.8392.
2. **Convert the Problem**: Use Z-tables or software to convert the probability statement to Z-scores.
3. **Find the Critical Value**: Look up the cumulative probability in the Z-table to find the corresponding Z-score for \(c\).
### Visual Representation
For a visual learner, imagine a standard normal curve:
- The area under the curve to the left of \(Z = -1.05\) plus the area under the curve between \(Z = -1.05\) and \(Z = c\) adds up to 0.8392.
- The Z-table or computational tools can help in determining the critical Z-value \(c\) that corresponds to an area under the curve equating to 0.8392 when combined with the area to the left of -1.05.
### Conclusion
Given the nature of the standard normal distribution, finding the exact critical value \(c\) typically involves some calculations or the use of statistical software or Z-tables. This solution provides a foundational understanding of how to approach problems related to the Z-distribution and probabilities within specific ranges.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2561c632-65dd-4d60-9cc7-c4695e3617a7%2F03cb7586-1244-41a7-a78a-8646dee36ec0%2Fc3iapnu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Value of \(c\)
In this exercise, we aim to determine the value of \(c\) given the following probability statement:
\[P(-1.05 \leq Z \leq c) = 0.8392\]
This problem involves finding the value of \(c\) in a standard normal distribution (Z-distribution) that satisfies the given probability.
- **Z** refers to the standard normal random variable.
- **P** denotes probability.
- \([-1.05 \leq Z \leq c]\) represents the range of Z-scores we are interested in.
- \(0.8392\) is the cumulative probability for that range.
#### Step-by-Step Solution
To solve this, follow these steps:
1. **Understand the Problem**: The given information tells us that the probability that Z lies between -1.05 and \(c\) is 0.8392.
2. **Convert the Problem**: Use Z-tables or software to convert the probability statement to Z-scores.
3. **Find the Critical Value**: Look up the cumulative probability in the Z-table to find the corresponding Z-score for \(c\).
### Visual Representation
For a visual learner, imagine a standard normal curve:
- The area under the curve to the left of \(Z = -1.05\) plus the area under the curve between \(Z = -1.05\) and \(Z = c\) adds up to 0.8392.
- The Z-table or computational tools can help in determining the critical Z-value \(c\) that corresponds to an area under the curve equating to 0.8392 when combined with the area to the left of -1.05.
### Conclusion
Given the nature of the standard normal distribution, finding the exact critical value \(c\) typically involves some calculations or the use of statistical software or Z-tables. This solution provides a foundational understanding of how to approach problems related to the Z-distribution and probabilities within specific ranges.
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