Police Academy Acceptance ExamsTo qualify for a police

Step 1 of 2

We are asked to find the cutoff score if only the top 20% of the applicants are selected.

We have given scores \(\mu=64\) and \(\sigma=9\)

Assume the variable is normally distributed.

Let \(X\) denote the score.

\(\begin{array}{l} P\left(X>X_{\text {cutoff }}\right)=20 \%=0.2 .\\ \begin{array}{l} P\left(X>X_{\text {cutoff }}\right)=1-P\left(X<X_{\text {cutoff }}\right) \\ P\left(X<X_{\text {cutoff }}\right)=1-P\left(X>X_{\text {cutoff }}\right) \\ P\left(X<X_{\text {cutoff }}\right)=1-0.2=0.8 \end{array} \end{array}\)