Using samples of 200 credit card statements, an Auditor found the following: ---

ID: 360370 • Letter: U

Question

Using samples of 200 credit card statements, an Auditor found the following:

---Sample Number: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Number of Errors: 27 23 23 28 22 25 35 33 27 27 34 27 33 21 25

Determine lower and upper control limits for the fraction of errors using three-sigma limits.

Question 8 options:

.075 , .197

.088 , .185

.063 , .209

.039 , .233

None of the Above

.075 , .197

.088 , .185

.063 , .209

.039 , .233

None of the Above

Given are :

Sample size = n = 200

Number of samples = 15

Thus total number of statements = Sample size x Number of statements = 200 x 15 = 3000

Total number of errors

= 27 + 23 + 23 + 28 +22 + 25 + 35 + 33 + 27 + 27 + 34 + 27 + 33 + 21 + 25 = 410

Therefore ,

Proportion of error = pbar = 410 / 3000 =0.1366

We need to construct Upper and Lower control Limits of a p chart to determine control limits for the fraction of errors using 3 sigma limits

Thus ,

Upper control Limit = Pbar + 3 x Square root ( pbar x ( 1 – pbar)/n)

= 0.1366 + 3 x Square root ( 0.1366 x 0.8634 /15)

= 0.1366 + 3 x 0.0886

= 0.1366 + 0.2658

= 0.4024

Lower Control Limit = Minimum ( 0, Pbar – 3 x Square root ( pbar x ( 1 – pbar)/n)

= Minimum ( 0, 0.1366 – 3 x 0.0886)

= Minimum ( 0 , - 0.1292)

= 0

Thus Answer would be “None of the above “

ANSWER : NONE OF THE ABOVE

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