Question

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.

Answer 1

Answer:

X₀ = 71.65

Step-by-step explanation:

given,

mean (μ ) = 64

standard deviation (σ) = 9

                                 σ²  = 81

selected candidate are top 20 % candidate

P( X > X₀)  = 0.2

$P( Z > \dfrac{X_0-\mu}{\sigma}) = 0.2$

$P( Z > \dfrac{X_0-64}{9})= 0.2$

P( Z > Z₀)  = 0.2

$Z_0 = 0.85 = \dfrac{X_0-64}{9}$

X₀ = 71.65

Hence, the cut off score is equal to X₀ = 71.65