Question

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 32 to 47 minutes. Test results for three participants were: Armand, a mean of 36.0 minutes and a standard deviation of 3.0 minutes; Jerry, a mean of 37.0 minutes and a standard deviation of 2.0 minutes; and Melissa, a mean of 39.5 minutes and a standard deviation of 3.2 minutes.

a.Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Participants Cpk Cp Capable ?

Armand

Jerry

Melissa

b.Can the value of the Cpk exceed the value of Cp for a given participant?

Yes

No

Answer 1

1. Cpk = MIN(UPPER LIMIT - MEAN / 3 * STANDARD DEVIATION, MEAN - LOWER LIMIT / 3 * STANDARD DEVIATION)

ARMAND

Cpk = MIN(47 - 36 / 3 * 3, 36 - 32 / 3 * 3)

Cpk = MIN(1.2222, 0.4444)

Cpk = 0.44

JERRY

Cpk = MIN(47 - 37 / 3 * 2, 37 - 32 / 3 * 2)

Cpk = MIN(1.6667, 0.8333)

Cpk = 0.83

MELLISA

Cpk = MIN(47 - 39.5 / 3 * 3.2, 39.5 - 32 / 3 * 3.2)

Cpk = MIN(0.7813, 0.7813)

Cpk = 0.78

None of the participants are capable, since we need atkeast a Cpk of 1 to be barely capable.

2. No, Cpk value cannot exceed Cp value since index is a non centered process.