Suppose you want to find out the grade you need to be in the

Suppose you want to find out the grade you need to be in the top 18% of your class on an exam. From past experience your teacher estimates the mean will be 75 and the standard deviation will 10. What will be the minimum score needed to be in the top 18% of your class?

Solution

Normal Distribution
Mean ( u ) =75
Standard Deviation ( sd )=10
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z < x ) = 0.82
Value of z to the cumulative probability of 0.82 from normal table is 0.915
P( x-u/s.d < x - 75/10 ) = 0.82
That is, ( x - 75/10 ) = 0.92
--> x = 0.92 * 10 + 75 = 84.15