A professor in a large Statistics class has a grading policy

A professor in a large Statistics class has a grading policy such that only the 15% of the students with the highest scores will receive the grade A. The mean score for the class is 72 with a standard deviation of 6. Assuming that all the grades for this class follow a normal distribution, what is the minimum score that a student in this class has to get to receive an A grade?

Solution

Normal Distribution
Mean ( u ) =72
Standard Deviation ( sd )=6
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.15
Value of z to the cumulative probability of 0.15 from normal table is 1.04
P( x-u/ (s.d) > x - 72/6) = 0.15
That is, ( x - 72/6) = 1.04
--> x = 1.04 * 6+72 = 78.216                  

minimum score that a student in this class has to get to receive an A grade
is ~78.22