A certain population is normally distributed with a mean of 138 and a standard deviation of 10. How many standard deviations from the mean is a person in the population with a value of 98. (That is find the z-score).
A certain population is normally distributed with a mean of 138 and a standard deviation of 10. How many standard deviations from the mean is a person in the population with a value of 98. (That is find the z-score).
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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Transcribed Image Text:The Z-score tells you the number of standard deviations away from the mean (and
X-μ
can be used to find the
in what direction) a data value is. The formula: Z
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.
σ
The formula X = μ+Z. 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 138 and a standard
deviation of 10.
How many standard deviations from the mean is a person in the population with a
value of 98. (That is find the z-score).
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