After a number of complaints about its directory assistance, a telephone company examined samples of calls to determine the frequency of wrong numbers given to callers. Each sample consisted of 117 calls.
SAMPLE
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Number of errors 4 3 5 6 1 6 5 2 5 10 3 2 5 2 6 4
a. Determine 95 percent limits. (Do not round your intermediate calculations. Round your final answers to 3 decimal places.)
UCL ___________
LCL ___________
Expert Answer
bar{p} = total no of defectives/total no of observations = 69/(117*16) =0.0369
Contro limits:
UCL = bar{p}+zsqrt{frac{bar{p}(1-bar{p})}{n}}
LCL = bar{p}-zsqrt{frac{bar{p}(1-bar{p})}{n}}
Z = 1.64
n = 117
0.0369(1 – 0.0369) LCL = 0.0369 _ 1.64 *
LCL = 0.008
LCL = 0.0369+1.64*sqrt{frac{0.0369*(1-0.0369)}{117}}
UCL = 0.065