For a population of exam scores, a score of x=58 corresponds to z=+0.50 and a score of x=46 corresponds to z=-1.00.  Find the mean and the standard deviation for the population.

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lemjay | High School Teacher | (Level 3) Senior Educator

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To solve apply the formula:


z -- z-score ,
x -- raw score,
`nu` -- mean and
`sigma` -- standard deviation

So, plug-in z=0.5, x=58 to the formula.


`0.5sigma=58-nu`     (Let this be EQ1.)

Also, plug-in z=-1 and x=46 to the formula too.



`sigma=-46+nu`       (Let this be EQ2.)

Then, substitute EQ2 to EQ1 in order to express EQ1 with nu only.







Then, plug-in this value to EQ2.




Hence, the mean is 54 and the standard deviation is 8.

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