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 45 minutes. Test results for three participants were: Armand, a mean of 39.0 minutes and a standard deviation of 3.0 minutes; Jerry, a mean of 35.0 minutes and a standard deviation of 2.0 minutes, and Melissa, a mean of 38.5 minutes and a standard deviation of 3.0 minutes. a.Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Сph Participants Armand Jerry Melissa Capable ? (Click to select) (Click to select) (Click to select) b.Can the value of the Cpk exceed the value of Cp for a given participant? Yes O No

Answer 1

CPK = MINIMUM((UPPER SPECIFICATION - MEAN) / 3 * STANDARD DEVIATION), (MEAN - LOWER SPECIFICATION) / 3 * STANDARD DEVIATION)
CP = (UPPER SPECIFICATION - LOWER SPECIFICATION) / (6 * STANDARD DEVIATION)

UPPER SPECIFICATION = 45
LOWER SPECIFICATION = 32

ARMAND

MEAN = 39
STDEV = 3

CPK = MIN((45 - 39) / (3 * 3), (39 - 32) / (3 * 3)) = MIN(0.67, 0.78) = 0.67
CP = (45 - 32) / (6 * 3) = 0.72

NO

JERRY

MEAN = 35
STDEV = 2

CPK = MIN((45 - 35) / (3 * 2), (35 - 32) / (3 * 2)) MIN(1.67, 1) = 0.5
CP = (45 - 32) / (6 * 2) = 1.08

YES, 3 SIGMA CAPABLE

MELLISA

STDEV = 3

CPK = MIN((45 - 38.5) / (3 * 3), (38.5 - 32) / (3 * 3)) = MIN(0.72, 1) = 0.72
CP = (45 - 32) / (6 * 3) = 0.72

NO