standard deviation is 700.
2400 is (3100 - 2400) / 700 = 1 standard deviation from the mean in a negative direction.
that makes the z-score equal to -1.
with z-scores, the mean is 0 and the z-score is the number of standard deviations away from the mean.
the formula is z = (x-m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
the formula becomes z = (2400 - 3100)/700 = -700/700 = -1
to find the percentage of employees that earn more than a z-score of -1, look up in the z-score table for a rate (rate = % / 100) to the left of a z-score of -1.
then take 1 minus that rate for a rate to the right of a z-score of -1.
if you used the table linked to below, you would have found the rate to the left of the z-score of -1 equal to .1587 and then gotten the rate to the right of the z-score of -1 equal to 1 - .1587 = .8413.
http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
alternatively use a calculator that goes normal distribution type problems.
i used the following calculator.
http://davidmlane.com/hyperstat/z_table.html
if allows me to find the rate to the left of or to the right of a particular z-score or in between 2 z-scores or outsides of 2 z-scores.
very nice calculator.
i got a rate of .8413
that means that 84.13% of the employees earn more than 2400 per month.
the number of employees that earn more than 2400 per month would be equal to 5000 * .8413 = 4206.5 which would be rounded to 4206 or 4207.
by convention of mathematical rounding rules, you would round to 4207.
the same calculator can be used with raw scores or z-scores.
with z-scores, mean is 0 and standard deviation is 1.
with raw scores, mean is 3100 and standard deviation is 700.
results are shown below:
the same calculator can be used to find the area from the z-score or the z-score from the area.
it can do the same using the raw mean score and standard deviation as well.
nice calculator.
even gives you a picture of the area under the distribution curve that it calculated for you.
use of the table rather than the calculator would have given you a result as shown below.
it's more work, but you get the same answer if you do it right.
the row heading would -1.0 and the column heading would be .00
add them together and you get a z-score of -1.00.