Satatistics

Question

the local police force gives all applicants an entrance exam and accepts only those applicants who score in the top 15% on this test. If the mean score this year is 87 and the standard deviation is 8, would an individual with a score of 110 be accepted?

Answer 1

You need to calculate the z-score which is the (tested value - mean)/SD.

 

z-score = 110-87 / 8 = 23/8 = 3.875

 

That means the score of 110 is 3.875 SDs away from the mean.  Looking at our z-score table, this is well into the 99th percentile.  Since you need to be in the 85th percentile (top 15% = 85th percentile) to pass, a 110 will be accepted.