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don't understand how that would not be the top 5%

don't understand how that would not be the top 5%

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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I really thought it was c-2.33, but don't understand how that would not be the top 5%

**Interactive Normal Distribution Graph** Please move the mouse slowly over the distribution. You do not need to drag the mouse to observe the ranges, which represent z-scores corresponding to the following percentages: 90%, 95%, 99%, and 99.9%. **Graph Details:** The graph displays a normal distribution curve, which is a symmetrical, bell-shaped curve that represents the distribution of many types of data. This specific curve highlights the percentage of data contained within certain standard deviations (z-scores) from the mean. - The mean of the distribution is indicated in the center of the horizontal axis at 0. - The horizontal axis displays standard deviations (z-scores) ranging from -3.29 to +3.29. - The highest point of the curve, corresponding to 99.9%, is located at the mean (0) on the horizontal axis. By moving your mouse along the curve, you will be able to see different critical values that help in understanding the spread and probability associated with the normal distribution. Remember that these z-scores are crucial in statistical analyses, such as hypothesis testing and confidence interval estimation.
Transcribed Image Text:**Interactive Normal Distribution Graph** Please move the mouse slowly over the distribution. You do not need to drag the mouse to observe the ranges, which represent z-scores corresponding to the following percentages: 90%, 95%, 99%, and 99.9%. **Graph Details:** The graph displays a normal distribution curve, which is a symmetrical, bell-shaped curve that represents the distribution of many types of data. This specific curve highlights the percentage of data contained within certain standard deviations (z-scores) from the mean. - The mean of the distribution is indicated in the center of the horizontal axis at 0. - The horizontal axis displays standard deviations (z-scores) ranging from -3.29 to +3.29. - The highest point of the curve, corresponding to 99.9%, is located at the mean (0) on the horizontal axis. By moving your mouse along the curve, you will be able to see different critical values that help in understanding the spread and probability associated with the normal distribution. Remember that these z-scores are crucial in statistical analyses, such as hypothesis testing and confidence interval estimation.
### Problem Statement **Question:** What is the z-value for a one-tail (upper) probability of 5%? **Answer Choices:** a. 1.65 b. 1.96 c. 2.33 d. 3.29 **Feedback:** An incorrect answer is selected (option d). ### Explanation The correct answer for the z-value corresponding to a one-tail (upper) probability of 5% is option a, 1.65. ### Detailed Solution In statistics, the z-value or z-score represents the number of standard deviations a data point is from the mean. The z-value can be found using the standard normal distribution table or an online calculator. For a one-tail upper probability of 5%, the z-value is 1.65. This means that 95% of the data falls below this z-score and 5% falls above it. **Common Mistake:** Choosing a higher z-value such as 3.29 may result from confusing the tail probability with a more extreme percentage. ### Graphical Representation While the image does not contain any graphical elements, a graph of the standard normal distribution could help illustrate this concept: - The standard normal distribution is a bell-shaped curve centered at zero. - The area under the curve corresponds to the probability. - For a one-tail upper probability of 5%, the area to the right of the z-value (1.65) represents 5% of the total area under the curve. If a graph were present, it would show the curve with a shaded area to the right of the z-score of 1.65, representing 5%. It is important to use tables or software accurately to find critical values in statistics.
Transcribed Image Text:### Problem Statement **Question:** What is the z-value for a one-tail (upper) probability of 5%? **Answer Choices:** a. 1.65 b. 1.96 c. 2.33 d. 3.29 **Feedback:** An incorrect answer is selected (option d). ### Explanation The correct answer for the z-value corresponding to a one-tail (upper) probability of 5% is option a, 1.65. ### Detailed Solution In statistics, the z-value or z-score represents the number of standard deviations a data point is from the mean. The z-value can be found using the standard normal distribution table or an online calculator. For a one-tail upper probability of 5%, the z-value is 1.65. This means that 95% of the data falls below this z-score and 5% falls above it. **Common Mistake:** Choosing a higher z-value such as 3.29 may result from confusing the tail probability with a more extreme percentage. ### Graphical Representation While the image does not contain any graphical elements, a graph of the standard normal distribution could help illustrate this concept: - The standard normal distribution is a bell-shaped curve centered at zero. - The area under the curve corresponds to the probability. - For a one-tail upper probability of 5%, the area to the right of the z-value (1.65) represents 5% of the total area under the curve. If a graph were present, it would show the curve with a shaded area to the right of the z-score of 1.65, representing 5%. It is important to use tables or software accurately to find critical values in statistics.
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