The verbal part of the Graduate Record Exam GRE has a m of 5

The verbal part of the Graduate Record Exam (GRE) has a m of 500 and s = 100. Use the normal distribution and the formulas and steps necessary to answer the following questions and show work:

If you wanted to select only students at or above the 87th percentile, what GRE score would you use as a cutoff score (i.e. what GRE score corresponds to this percentile)?

Solution

Normal Distribution
Mean ( u ) =500
Standard Deviation ( sd )=100
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.87
Value of z to the cumulative probability of 0.87 from normal table is -1.13
P( x-u/ (s.d) > x - 500/100) = 0.87
That is, ( x - 500/100) = -1.13
--> x = -1.13 * 100+500 = 387.4