Question 1185999
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In a population distribution, a score of X = 28 corresponds to a z = -6.00 and 
a score of 66 corresponds to a z = 3.50. Find the mean and standard deviation of the population.
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<pre>
Write equations based on the definitions of the mean "m", standard score "z" 
and standard deviation "s"

    {{{(28-m)/s}}} = -6       (1)

    {{{(66-m)/s}}} = 3.50     (2)


Simplify and write as a system of linear equations

    28 - m = -6s              (3)

    66 - m = 3.5s             (4)


Subtract equation (3) from equation (2)

    66 - 28 = 3.5s - (-6s),

      38    =     9.5s

       s    =     38/9.5 

       s    =       4.


Half of the problem is just solved: the value of s = 4 is found.


Now substitute s= 4 into equation (3)


    28 - m = -6*4

    28 - m = -24

    28 + 24 = m

       m    = 52.



<U>ANSWER</U>.  m = 52;  s = 4.
</pre>

Solved.