The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 544 and the standard deviation was 72. If the board wants to set the passing score so that only the best 80% of all applicants pass, what is the passing score? Assume that the scores are normally distributed.
+6251 \(\mbox{You want a score }G \mbox{ such that }\Phi\left(\dfrac{G-544}{72}\right)=0.2 \\ \mbox{where }\Phi(x) \mbox{ is the CDF of the standard normal.}\\ \mbox{Using the trusty table we find that }\\ \Phi^{-1}(0.2)=-0.841621 \mbox{ so}\\ \dfrac {G-544}{72}=-0.841621 \\ G = 483.4\)
.
