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A population of porcupines has a normally distributed lifespan with a mean of 5.5 years and a standard deviation of 1.0 years.  We collected a sample of 12 porcupines and calculated their mean lifespan to be x¯ = 6.2 years.  Which of the standard normal distributions below represent our observed sample mean (purple dashed line) compared to the sampling distribution of sample means (red line) for a sample size of 12? a. A b. B c. C d. D

A population of porcupines has a normally distributed lifespan with a mean of 5.5 years and a standard deviation of 1.0 years.  We collected a sample of 12 porcupines and calculated their mean lifespan to be x¯ = 6.2 years.  Which of the standard normal distributions below represent our observed sample mean (purple dashed line) compared to the sampling distribution of sample means (red line) for a sample size of 12? a. A b. B c. C d. D

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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 A population of porcupines has a normally distributed lifespan with a mean of 5.5 years and a standard deviation of 1.0 years.  We collected a sample of 12 porcupines and calculated their mean lifespan to be x¯ = 6.2 years.  Which of the standard normal distributions below represent our observed sample mean (purple dashed line) compared to the sampling distribution of sample means (red line) for a sample size of 12?

a. A

b. B

c. C

d. D

### Understanding Z-Scores and Probability Distributions In this section, we will explore a set of graphs that illustrate the concept of Z-scores and their corresponding positions within a standard normal distribution curve. #### Graph Descriptions Each graph (A, B, C, and D) displays a standard normal distribution curve (in red), which represents a bell-shaped probability distribution that is symmetric around the mean (μ = 0) with a standard deviation (σ = 1). These distributions are used to calculate probabilities and identify outliers in data sets. Each graph includes a vertical dashed line (in purple) set at different Z-score values, highlighting how the Z-score relates to the distribution curve. - **Graph A:** - The vertical purple dashed line is positioned at approximately Z = 0.5. - This indicates a Z-score of 0.5, which means the point is 0.5 standard deviations above the mean of the distribution. - **Graph B:** - The vertical purple dashed line is positioned at approximately Z = 1. - This indicates a Z-score of 1, meaning the point is 1 standard deviation above the mean of the distribution. - **Graph C:** - The vertical purple dashed line is positioned at approximately Z = 1.5. - This indicates a Z-score of 1.5, meaning the point is 1.5 standard deviations above the mean of the distribution. - **Graph D:** - The vertical purple dashed line is positioned at approximately Z = 2. - This indicates a Z-score of 2, meaning the point is 2 standard deviations above the mean of the distribution. #### Interpreting Z-Scores The Z-score is a measure of how many standard deviations an element is from the mean. It is used in statistics to determine the relative position of a data point within a data set. - A positive Z-score indicates that the data point is above the mean. - A negative Z-score indicates that the data point is below the mean. - A Z-score of 0 indicates that the data point is exactly at the mean. #### Application Understanding and visualizing Z-scores in the context of a normal distribution is crucial in fields such as psychology, finance, and natural sciences, where it is essential to determine how unusual or typical a particular value is within a given set of data. By examining the area under the
Transcribed Image Text:### Understanding Z-Scores and Probability Distributions In this section, we will explore a set of graphs that illustrate the concept of Z-scores and their corresponding positions within a standard normal distribution curve. #### Graph Descriptions Each graph (A, B, C, and D) displays a standard normal distribution curve (in red), which represents a bell-shaped probability distribution that is symmetric around the mean (μ = 0) with a standard deviation (σ = 1). These distributions are used to calculate probabilities and identify outliers in data sets. Each graph includes a vertical dashed line (in purple) set at different Z-score values, highlighting how the Z-score relates to the distribution curve. - **Graph A:** - The vertical purple dashed line is positioned at approximately Z = 0.5. - This indicates a Z-score of 0.5, which means the point is 0.5 standard deviations above the mean of the distribution. - **Graph B:** - The vertical purple dashed line is positioned at approximately Z = 1. - This indicates a Z-score of 1, meaning the point is 1 standard deviation above the mean of the distribution. - **Graph C:** - The vertical purple dashed line is positioned at approximately Z = 1.5. - This indicates a Z-score of 1.5, meaning the point is 1.5 standard deviations above the mean of the distribution. - **Graph D:** - The vertical purple dashed line is positioned at approximately Z = 2. - This indicates a Z-score of 2, meaning the point is 2 standard deviations above the mean of the distribution. #### Interpreting Z-Scores The Z-score is a measure of how many standard deviations an element is from the mean. It is used in statistics to determine the relative position of a data point within a data set. - A positive Z-score indicates that the data point is above the mean. - A negative Z-score indicates that the data point is below the mean. - A Z-score of 0 indicates that the data point is exactly at the mean. #### Application Understanding and visualizing Z-scores in the context of a normal distribution is crucial in fields such as psychology, finance, and natural sciences, where it is essential to determine how unusual or typical a particular value is within a given set of data. By examining the area under the
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