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 30 to 47 minutes. Test results for three participants were: Armand, a mean of 37.0 minutes and a standard deviation of 3.0 minutes; Jerry, a mean of 34.0 minutes and a standard deviation of 2.0 minutes; and Melissa, a mean of 38.5 minutes and a standard deviation of 2.4 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	.89 .89 Incorrect		No Correct
Jerry	.82 .82 Incorrect		No Correct
Melissa		1.18 1.18 Correct	No Correct

b.Can the value of the C_pk exceed the value of C_p for a given participant?

• Yes

• No

Answer 1

a)

Participants	Cpk	Cp	Capable?
Armand	0.78	0.94	No
Jerry	0.67	1.42	No
Melissa	1.18	1.18	No

Cpk for Armand = Min[(37-30)/(3*3), (47-37)/(3*3)]

=Min(7/9,10/9) = 7/9 = 0.78 (Rounded to 2 decimal places)

Cpk fpr Jerry = Min[(34-30)/(3*2), (47-34)/(3*2)]

=Min(4/6,13/6) = 4/6 = 0.67 (Rounded to 2 decimal places)

Cpk fpr Melissa= Min[(38.5-30)/(3*2.4), (47-38.5)/(3*2.4)]

=Min(1.180555556,1.180555556) = 1.180555556 = 1.18 (Rounded to 2 decimal places)

Cp for Armand = (47-30)/(6*3) = 0.94

Cp for jerry = (47-30)/(6*2) = 1.42

Cp for Melissa = (47-30)/(6*2.4) = 1.18

No participants are capable as Cpk is less than 1.33

b)

No, the value of Cpk can not exceed the value of Cp for a given participant