Question

The defect rate for data entry of insurance claims has historically been about 1.00​%. This exercise contains only parts​ a, b,​ c, d, and e. ​a) If you wish to use a sample size of 200​, the 3​-sigma control limits are​: UCL Subscript pequals nothing ​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). LCL Subscript pequals nothing ​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). ​b) If the sample size is 100​, the 3sigma control limits are​: UCL Subscript pequals nothing ​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). LCL Subscript pequals nothing ​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). ​c) If the sample size is 200​, the 2sigma control limits are​: UCL Subscript pequals nothing ​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). LCL Subscript pequals nothing ​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). ​d) If the sample size is 100​, the 2sigma control limits are​: UCL Subscript pequals nothing ​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). LCL Subscript pequals nothing ​(enter your response as a number between 0 and​ 1, rounded to three decimal​ places). ​e) What happens to ModifyingAbove sigma with caret Subscript p when the sample size is​ larger? When the sample size is​ larger, ModifyingAbove sigma with caret Subscript p is

Answer 1

p-bar = 1-Defect % = 1-1% = 0.99

sigma (s) = sqrt(p-bar*(1-p-bar)/n)

UCL = p-bar + z*sigma

LCL = p-bar - z*sigma

a) n = 200, z = 3 (3 -sigma)

sigma = sqrt(0.99*(1-0.99)/200) = 0.007

UCL = 0.99 + 3*0.007 = 1.01. Hence 1.00

LCL = 0.99 - 3*0.007 = 0.97

b) n = 100, z = 3 (3 -sigma)

sigma = sqrt(0.99*(1-0.99)/100) = 0.010

UCL = 0.99 + 3*0.010 = 1.02. Hence 1.00

LCL = 0.99 - 3*0.010 = 0.96

c) n = 200, z = 2 (2 -sigma)

sigma = sqrt(0.99*(1-0.99)/200) = 0.007

UCL = 0.99 + 2*0.007 = 1.00

LCL = 0.99 - 3*0.007 = 0.98

d) n = 100, z = 2 (2 -sigma)

sigma = sqrt(0.99*(1-0.99)/100) = 0.010

UCL = 0.99 + 2*0.010 = 1.01

LCL = 0.99 - 3*0.007 = 0.97