Question $7$: $[20$pt$]$

As part of an insurance company$$s training program, participants learn how to conduct an analysis of clients$$ insurability. The goal is to have participants achieve a time in the range of $30$ to $45$ minutes. Test results for three participants were: Armand, a mean of $38$ minutes and a standard deviation of $3$ minutes; Jerry, a mean of $37$ minutes and a standard deviation of $2\mathrm{.}5$ minutes; and Melissa a mean of $37\mathrm{.}5$ minutes and a standard deviation of $1\mathrm{.}8$ minutes.

a$.[12$pt$]$ Which of the participants would you judge to be capable? Explain.

b$.[8$pt$]$ Can the value of the Cpk exceed the value of Cp for a given participant? Explain.