Because they allow for a comparison between two scores that do not belong to the same normal distribution, z-scores are significant.
They are also employed to determine the likelihood that a z-score will occur inside a normal distribution. A negative z-score indicates that the raw data is smaller than the mean.
What Is a Z-Score?
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score.
A Z-score of zero means the data point's score is the same as the mean score.
Converting to z-Scores Conceptual Overview: Explore how an original or "raw" score can be expressed as a 7-score using the mean and standard deviation of the variable. The dot plot below shows the sizes for five classes with a mean of 44 and standard deviation of 8. The dynamic equation shows the mathematical conversion to z-scores in real-time. Drag the vertical line to see the corresponding 2-score for each possible class size. 2 42-44 = 8 -0.25 s x = 42 32 54 mean x = 44 z = -0.25 -1.50 0.25 1.24 mean z=0 Created by Gary H. McClelland, Professor Emeritus University of Colorado Boulder Cengage Learning. All Rights Reserved 1. Make sure the green line is on the mean value of x = 44. Next, move the green line one standard deviation to the right. What z-score is associated with this value?
First you have multiply 6 by both 3x and 8 6*3x = 18x 6*8= 48 18x + 48 + 32 + 12x now combine like terms 18x + 12x = 30x 48 + 32 = 80 so 30x + 80 is your answer
Since each one of these methodologies are not related to one another and they do not need to be chosen in any order or consecutively then the possible outcomes would only need to be added all together to calculate the total possible outcomes. Since each outcome is independent. Therefore,
m1 = 5 outcomes
m2 = 2 outcomes
m3 = 4 outcomes
m4 = 4 outcomes
5 + 2 + 4 + 4 = 15
we can see that there are a total of 15 possible outcomes
