If the company wishes to set 99.7% control limits based on samples of size 500, what would these limits be?

A computer diskette manufacturer is concerned that some diskettes have bad sectors that would cause a diskette to hold less information than it was intended to hold. In the past, only 5% of these diskettes have had bad sectors. If the company wishes to set 99.7% control limits based on samples of size 500, what would these limits be?If the company wishes to set 99.7% control limits based on samples of size 500, what would these limits be?
Using the normal approximation of the binomial:


the probability of a bad sector = 0.05=p; prob of no bad sector=q=0.95


z = (p-0.05)/ sqrt(p*q/500)


99.7% implies a 3-sigma confidence interval.





3*sqrt(0.05*0.95/500) = 0.02924





[ 0.05-0.02924, 0.05+0.02924], the proportion of bad diskettes will lie between these limits 99.7% of the time for batches of 500.