For a spinning process it is known that the average yarn cou

For a spinning process, it is known that the average yarn count (

As upper and lower specification limit in interval form is (31.3, 32.7) we find that the mean mu lies within this interval.

But mean is not the midpoint here

Thus mean as per conf interval = 32 whereas actual mu = 32.5

If the confidence interval is improved for mean then margin of error should be 32.7-32.5 = 0.2

Z = 1 as sigma = 0.2

Z = 32.5-32/0.2/rtn

if margin of error is 0.2

then 2.5 (rtn) = 0.2

By increasing sample size this can be done.