To qualify for a police academy, applicants are given a test of physical fitness. The scores are normally distributed with a mean of 64 and a standard deviation of 9. If only the top 20% of all applicants are selected, find the cut off score. Round up your answer to the nearest integer.
Accepted Solution
A:
Answer:X₀ = 71.65Step-by-step explanation:given,mean (μ ) = 64standard deviation (σ) = 9 σ² = 81selected candidate are top 20 % candidate P( X > X₀) = 0.2[tex]P( Z > \dfrac{X_0-\mu}{\sigma}) = 0.2[/tex][tex]P( Z > \dfrac{X_0-64}{9})= 0.2[/tex]P( Z > Z₀) = 0.2[tex]Z_0 = 0.85 = \dfrac{X_0-64}{9}[/tex]X₀ = 71.65Hence, the cut off score is equal to X₀ = 71.65