I need questions A and B answered Thanks Problem 10 As part

I need questions A and B answered, Thanks.

Problem 10 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 2.5 minutes; and Melissa, a mean of 37.5 minutes and a standard deviation of 1.8 minutes. a. Which of the participants would you judge to be capable? Explain. b. Can the value of the Cpk exceed the value of Cp for a given participant? Explain.

Solution

Answer:

a. Out of 3 participants, Melissa is capable. The reason is the mean is 37.5 minutes & standard deviation is 1.8 minutes. These figures reflects that Melissa was taking an average of 37.5 minutes per customer and difference in time taken for each customer is minimum, it is evident from the value of standard deviation which shows his consistent in duration taken of analysis.

Standard deviation is a measure of the dispersion of a set of data from its mean.

The other two participates have 37 & 38 minutes as a mean for each customer but their standard deviation is 2.5 & 3 minutes respectively. with reflects their inconsistent duration taken by them for the analysis of customer.

b. Yes the value of C_pk can exceed the value of C_p of a given participant when the participant were meeting the target consistently with minimum variation i.e., less standard deviation.

Where,

      C_p = Process capability. A simple straightforward indicator of process capability

     C_pk = Process capability index. Adjustment of C_p for the effect of non-centered distribution.

Additional Information: C_pk measures how near you are to your target and how regular you are to your average performance. A person may be executing with minimum variation, but he can be away from his target towards one of the allowable limit, which indicates lower C_pk, whereas C_p will be high. On the other option, a participate may be on \"mean\" exactly at the target, but the variation in execution is high (but still lower than the allowed range . In such case also C_pk will be lower, but C_p will be high.