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The Z-score tells you the number of standard deviations away from the mean (and in what direction) a data value is. The formula: Z = X can be used to find the Z-score for a single member of the population. Notice X - μ tells you the signed distance the data value (X) is from the mean. When you divide that the size of each chunk (the standard deviation) you are measuring the distance in units of the size of th standard deviations (how many standard deviations fit in the distance between the data value and the mean) - which gives you the Z-score. The formula X = μ + Zo can be used to find the value in the population when given the Z-score (signed number of standard deviations). Notice that Z. o tells you how far from the mean the data value is (since Z is the number of standard. deviations and is the size of each standard deviation the product tells the total distance). So adding t distance from the mean to the mean gives the location along the number line for the data value.

The Z-score tells you the number of standard deviations away from the mean (and in what direction) a data value is. The formula: Z = X can be used to find the Z-score for a single member of the population. Notice X - μ tells you the signed distance the data value (X) is from the mean. When you divide that the size of each chunk (the standard deviation) you are measuring the distance in units of the size of th standard deviations (how many standard deviations fit in the distance between the data value and the mean) - which gives you the Z-score. The formula X = μ + Zo can be used to find the value in the population when given the Z-score (signed number of standard deviations). Notice that Z. o tells you how far from the mean the data value is (since Z is the number of standard. deviations and is the size of each standard deviation the product tells the total distance). So adding t distance from the mean to the mean gives the location along the number line for the data value.

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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The Z-score tells you the number of standard deviations away from the mean (and in what direction) a data value is. The formula: Z = X can be used to find the Z-score for a single member of the population. Notice X - μ tells you the signed distance the data value (X) is from the mean. When you divide that by the size of each chunk (the standard deviation) you are measuring the distance in units of the size of the standard deviations (how many standard deviations fit in the distance between the data value and the mean) - which gives you the Z-score. The formula X = μ+Z-o can be used to find the value in the population when given the Z-score (signed number of standard deviations). Notice that Z. tells you how far from the mean the data value is (since Z is the number of standard deviations and is the size of each standard deviation the product tells the total distance). So adding the distance from the mean to the mean gives the location along the number line for the data value. A certain population is normally distributed with a mean of 173 and a standard deviation of 19. What is the data value in the population (X) if the Z-score is 0.56 standard deviations?
Transcribed Image Text:The Z-score tells you the number of standard deviations away from the mean (and in what direction) a data value is. The formula: Z = X can be used to find the Z-score for a single member of the population. Notice X - μ tells you the signed distance the data value (X) is from the mean. When you divide that by the size of each chunk (the standard deviation) you are measuring the distance in units of the size of the standard deviations (how many standard deviations fit in the distance between the data value and the mean) - which gives you the Z-score. The formula X = μ+Z-o can be used to find the value in the population when given the Z-score (signed number of standard deviations). Notice that Z. tells you how far from the mean the data value is (since Z is the number of standard deviations and is the size of each standard deviation the product tells the total distance). So adding the distance from the mean to the mean gives the location along the number line for the data value. A certain population is normally distributed with a mean of 173 and a standard deviation of 19. What is the data value in the population (X) if the Z-score is 0.56 standard deviations?
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