SOLUTION: 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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Question 1185999: 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
Answer by ikleyn(52775) About Me  (Show Source):
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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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Write equations based on the definitions of the mean "m", standard score "z" 
and standard deviation "s"

    %2828-m%29%2Fs = -6       (1)

    %2866-m%29%2Fs = 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.



ANSWER.  m = 52;  s = 4.

Solved.