Table 5.3

-Samples of 100 checks each were taken at a bank from an encoding machine (which records the amount of a check) over a five-day period. Details are summarized in Table 5.3. If the bank were to use the average proportion defective from these five samples as the central line for a process control chart, what would be the central line?
A) less than or equal to 0.01
B) greater than 0.01 but less than or equal to 0.02
C) greater than 0.02 but less than or equal to 0.03
D) greater than 0.03

Question

Table 5.3
 
-Samples of 100 checks each were taken at a bank from an encoding machine (which records the amount of a check) over a five-day period. Details are summarized in Table 5.3. If the bank were to use the average proportion defective from these five samples as the central line for a process control chart, what would be the central line?
A) less than or equal to 0.01 
B) greater than 0.01 but less than or equal to 0.02 
C) greater than 0.02 but less than or equal to 0.03 
D) greater than 0.03

Quizplus · Accepted Answer

To find the central line for the process control chart, we need to take the average of the proportion defective for each of the five samples. The proportion defective is calculated by dividing the number of defective checks (those with encoding errors) by the total sample size (100 checks). From Table 5.3, we can see that the proportion defective for each sample ranges from 0.020 to 0.034, with a grand average of 0.026. Therefore, the average proportion defective from these five samples, which would be the central line for the process control chart, is greater than 0.02 but less than or equal to 0.03. The correct answer is C.

Table 5.3 -Samples of 100 Checks Each Were Taken at a Bank