Question 854621
Officer 1 gets 76 
Officer 2 gets 68
mean of all scores is 62 with standard deviation of 11.


z-score = (x-m) / s


x = the raw score of the officer taking the test.
m = the mean of all scores.
s = the standard deviation of all scores.


z-score for Officer 1 is (76-62)/11 = 14/11 = 1.28
z-score for Officer 2 is (68-62)/11 = 6/11 = .55


probability of getting a z-score less than 1.28 is .9.
probability of getting a z-score less than .71.


Officer 1 will get promoted.
Officer 2 will not.


you look up the z-scores in the z-score table and the table tells you the probability of getting a score less than that.


i used the ti-84 calculator, but you can get similar results with the following table:


<a href = "http://lilt.ilstu.edu/dasacke/eco148/ztable.htm" target = "_blank">http://lilt.ilstu.edu/dasacke/eco148/ztable.htm</a>


for example:


i looked for a z-score of 1.28


the left column will show me the row where 1.2 is and the 10th column for that row will give me the area under the distribution curve to the left of the z-score of 1.28 which is equal to 1.2 from the first column plus .08 from the 10th column to get 1.28.


the area shown there is .8997 which is rounded to .9.