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A data value of 99 corresponds to a standardized value of

A data value of 99 corresponds to a standardized value of

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Standardized Values in a Normal Distribution** When analyzing data, it's useful to standardize values to understand how they compare within the distribution's context. Refer to the following normal curve, which has a mean (μ) and a standard deviation (σ). ![Normal Curve Diagram](normal_curve.png) ### Description of the Diagram The diagram displays a normal distribution curve, with the peak representing the mean value. It highlights the area where 95% of the total observations fall, centered around the mean. This range spans from a value of 24 to 84 on the x-axis. ### Question A data value of 99 corresponds to a standardized value of: #### Answer Choices - a. 2. - b. 3. - c. None of these - d. 45. - e. 2.5. ### Explanation To find the standardized value (often referred to as a z-score), the following formula is used: \[ z = \frac{(X - \mu)}{\sigma} \] Where: - \( X \) is the data value (in this case, 99). - \( \mu \) is the mean. - \( \sigma \) is the standard deviation. Use this formula to determine which answer choice is correct. ### Select the correct answer and understand the computation: Please select one from the options provided based on your calculations. --- This task can help students understand the concept of z-scores and their significance in statistical analysis, enabling a consistent interpretation of data within a given distribution.
Transcribed Image Text:**Standardized Values in a Normal Distribution** When analyzing data, it's useful to standardize values to understand how they compare within the distribution's context. Refer to the following normal curve, which has a mean (μ) and a standard deviation (σ). ![Normal Curve Diagram](normal_curve.png) ### Description of the Diagram The diagram displays a normal distribution curve, with the peak representing the mean value. It highlights the area where 95% of the total observations fall, centered around the mean. This range spans from a value of 24 to 84 on the x-axis. ### Question A data value of 99 corresponds to a standardized value of: #### Answer Choices - a. 2. - b. 3. - c. None of these - d. 45. - e. 2.5. ### Explanation To find the standardized value (often referred to as a z-score), the following formula is used: \[ z = \frac{(X - \mu)}{\sigma} \] Where: - \( X \) is the data value (in this case, 99). - \( \mu \) is the mean. - \( \sigma \) is the standard deviation. Use this formula to determine which answer choice is correct. ### Select the correct answer and understand the computation: Please select one from the options provided based on your calculations. --- This task can help students understand the concept of z-scores and their significance in statistical analysis, enabling a consistent interpretation of data within a given distribution.
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