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 38.0 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 1.8 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			(Click to select)  No  Yes
Jerry			(Click to select)  Yes  No
Melissa			(Click to select)  No  Yes

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

• Yes

• No

Answer 1

Cp=(USL-LSL)/6*Sigma if mean is (30+47)/2 =38.5

Cpk= Min( USL-mean/ 3*sigma, mean-LSL/ 3*sigma)

Armand= Cpk =min(47-38/ 3*3, 38-30/3*3) = 8/9= .89 not capable

Jerry =Cpk =min(47-35/ 3*2, 35-30/3*2) = 5/6 =.82 not capable

Melissa = Cp =(47-30)/ 6*1.8=1.57 capable

b. No Cpk can not exceed the Cp due higher deviation (check formula )