document.write( "Question 1018967: I really need your help in solving this problem. I appreciate your time and efforts. Have a terrific day :) Here is the question:\r
\n" ); document.write( "\n" ); document.write( "In a population of exam scores, a score of X=48 corresponds to Z= +1.00 and a score of X = 36 corresponds to Z = - 0.50. Find the mean and standard deviation for the population. \n" ); document.write( "
Algebra.Com's Answer #634972 by mathmate(429)\"\" \"About 
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\n" ); document.write( "Question:
\n" ); document.write( "In a population of exam scores, a score of X=48 corresponds to Z= +1.00 and a score of X = 36 corresponds to Z = - 0.50. Find the mean and standard deviation for the population.
\n" ); document.write( "
\n" ); document.write( "Solution:
\n" ); document.write( "Using Z=(X-μ)/σ,
\n" ); document.write( "we substitute into the given data:
\n" ); document.write( "1.0=(48-μ)/σ
\n" ); document.write( "=>
\n" ); document.write( "μ+σ=48........(1)
\n" ); document.write( "-0.50=(36-μ)/σ
\n" ); document.write( "=>
\n" ); document.write( "μ-0.5σ=36 .....(2)
\n" ); document.write( "
\n" ); document.write( "(1)-(2)
\n" ); document.write( "1.5σ=12 =>σ=8.....(3)
\n" ); document.write( "
\n" ); document.write( "Substitute (3) in (1)
\n" ); document.write( "μ+8=48 => μ=40 ......(4)
\n" ); document.write( "
\n" ); document.write( "Check:
\n" ); document.write( "(48-40)/8=1
\n" ); document.write( "(36-40)/8=-0.5
\n" ); document.write( "so both are correct. \n" ); document.write( "
\n" );