You are trying to recruit the top talent. To measure the skills of applicants you use 3 test service providers: GRR, PSS, and LSP. The providers tell you the scores received by

candidates are normally distributed with the following characteristics:

• GRR: mean (μ) =800, standard deviation (σ) = 150
• PSS: mean (μ) = 1600, standard deviation (σ) =300
• LSP: mean (μ) =100, standard deviation (σ) =25

1. Two candidates, Luke and Darth apply for the same position. Luke took PSS and scored 2200, Darth took GRR and scored 1250.

a. What proportion of PSS takers scored higher than Luke? What proportion scored lower?

b. What proportion of GRR takers scored higher than Darth? What proportion scored lower?

2. R2D2 also applies for position. R2D2 takes LSP and scores 180.

a. What proportion of LSP takers scored above R2D2? What proportion scored lower?

3. Assuming the three tests are equally challenging, which candidate you would choose?