An auto dealer is looking to hire a mechanic who can perform inspections on vehicles. The goal is to have the potential hires examine a vehicle in 45 to 60 minutes. Too short a duration indicates problems may be missed and too long indicates a lack of skill. Three potential hires were tested. Test results for three participants were: Mario, with a mean of 51 minutes and a standard deviation of 3.2 minutes; Luigi, with a mean of 48 minutes and a standard deviation of 2.5 minutes; and Rosalina, with a mean of 52.5 minutes and a standard deviation of 2.5 minutes.
a. Which of the potential hires would you judge to be capable? Explain.
b. Can the value of the Cpk exceed the value of Cp for a given participant? Explain