Question

The average grade for an exam is 74, and the standard deviation is 7. If 12% of the class is given grade A, and the grades are curved to follow a normal distribution, what is the lowest possible grade A?

Answer 1

Standard Normal Distribution Table will be used to find the value of z for the required percentile. Supposed 12% of the class are to be awarded A's then z value is obtained at the 88th percentile from the Standard Normal Probability Table as follows .

0.8810 provides z= 1.18

then the neceresry score is obtained by setting

z= $\frac{x-the average}{standard deviation}$

x= the score to calculated

1.18= $\frac{x-74}{7}$

x= $({1.18\times7})+ 74 = 82.26$ ( rounded down)

x= 82 is the score required to receive an A.