Answer
mean = 250, standard deviation = 175.78
Work Step by Step
If a manager gets an "A" grade, they are in the top 10%. Another way of saying this is that they have a normal value of .9.
If a manager gets a "C" grade, they are in the bottom 10%. Another way of saying this is that they have a normal value of .1.
The formula for a manager with an "A" grade:
$(475-mean)/deviation = 1.28$
The formula for a manager with a "C" grade:
$(25-mean)/deviation = -1.28$
$(475-mean)/deviation = 1.28$ $(25-mean)/deviation = -1.28$
$(475-mean)/deviation = 1.28$ $-1*(25-mean)/deviation = -1*-1.28$
$(475-mean)/deviation = 1.28$ $(-25+mean)/deviation = 1.28$
$(475-mean)/deviation = (-25+mean)/deviation$
$475 - mean = mean - 25$
$475 - mean + mean + 25 = mean - 25 + mean + 25$
$500 = 2 * mean$
$mean = 250$
$(475-mean)/deviation = 1.28$
$(475-250)/deviation = 1.28$
$225/deviation = 1.28$
$225/deviation * deviation= 1.28* deviation$
$225 = 1.28 * deviation$
$225/1.28 = deviation$
$175.78 = deviation$
