Since about 95% of a normal distribution falls within two standard deviations of the mean 
, it follows that 5% lie outside this range, with 2.5% lying to either side of it.This means 
, with the remaining 2.5% lying above 
.
This means for a score to belong in the top 2.5%, it's corresponding z-score must be higher than 2.
Fred scores 13.1 on the test. The corresponding z-score is
which is barely higher than 2, but high enough to earn that certificate.
This means for a score to belong in the top 2.5%, it's corresponding z-score must be higher than 2.
Fred scores 13.1 on the test. The corresponding z-score is
which is barely higher than 2, but high enough to earn that certificate.
