Scores from a certain standardized test are normally distrib

Scores from a certain standardized test are normally distributed with a mean of 800 and a standard deviation of 55. What is the average of the scores that are at the 60th and 75th percentile?

A. 825.5 B. 837.5 C. 856 D. 940

Solution

AT 60 Percentile
P ( Z < x ) = 0.6
Value of z to the cumulative probability of 0.6 from normal table is 0.253
P( x-u/s.d < x - 800/55 ) = 0.6
That is, ( x - 800/55 ) = 0.25
--> x = 0.25 * 55 + 800 = 813.915                  
AT 75 Percentile
P ( Z < x ) = 0.75
Value of z to the cumulative probability of 0.75 from normal table is 0.674
P( x-u/s.d < x - 800/55 ) = 0.75
That is, ( x - 800/55 ) = 0.67
--> x = 0.67 * 55 + 800 = 837.07                  

Average of both = (813.915+  837.07 )/2 = 825.50