Question 1074409
mean is 3100
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.


<a href = "http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf" target = "_blank">http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf</a>


alternatively use a calculator that goes normal distribution type problems.


i used the following calculator.


<a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


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:


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<img src = "http://theo.x10hosting.com/2017/032702.jpg" alt="$$$" </>


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.


<img src = "http://theo.x10hosting.com/2017/032703.jpg" alt="$$$" </>


<img src ="http://theo.x10hosting.com/2017/032705.jpg" alt="$$$" </>


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.