Question 1207223
the calculator at <a hreef = "" target = "_blank"></a> can help you find the answer to these questions.


here are the results.


<img src = "http://theo.x10hosting.com/2024/050701.jpg">


<img src = "http://theo.x10hosting.com/2024/050702.jpg">


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this calculator can work directly off the raw scores or off the z-scores.


to show you how it works off the z-scores, we'll take the second problem that calculates the probability of between 4.2 and 83.


to work off z-scores, you set the mean to 0 and the standard deviation to 1.


you find the z-score for 4.2 and the z-score for 83.


z = (x-m)/s is the z-score formula.
z is the z-score.
x is the raw score.
m is the raw mean.
s is the standard deviation.


for raw score of 4.2, formula becomes z = (4.2 - 84.11) / 81.37 = -.982057 rounded to 6 decimal places.


for raw score of 83, formula becomes z = (83 - 84.11) / 81.37 = -.013641 rounded to 6 decimal places.


set the calculator mean to 0 and the calculator standard deviation to 1 and find the probability of getting a z-score between -.982057 and -.013641.


the results are shown below.


<img src = "http://theo.x10hosting.com/2024/050706.jpg">


the calculator tells you that the probability is .3325.
this is the same as the probability we got earlier when working directly with raw scores.
prior to the user of calculators, you has to get the z-score first and then work off the z-score.
the calculators do that work for you, but it's still useful to know how to work with the z-scores,