a Assuming that the distribution of the data is approximatel

a) Assuming that the distribution of the data is approximately normal, what proportion of the units would you expect to meet specifications of 323 and 337?

b)If the mean of the distribution shifts to 330, compute the probability that the shift will not be detected on the chart on the first subgroup plotted after the shift takes place. Assume no change in 3-sigma

c) Assuming the data are normal distribution, what proportion of non conforming units would be produced at this new value of the mean? (Use specifications limit from Prob. a)

R-9-15-0- 50-4700 17-80 11-12 9 9 5 5 5 5 50 05 50 55 05 0 277720527072525 ra -X082039 576355 78 7 2 4580101144 2 2 2 3 gm 123456 780012345

Solution

Mean of all x bars = 328.50

mu = 328.50

std dev = 3.5569

a) P(323

= 0.4394+0.4962

= 0.9356

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If mean = 330,

P(323<330<337) = P(-1.97

=2(0.4756)

= 0.9512

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If margin of error = +3 or -3 the units would be conforming

Or as per original mean

confidence interval = (328.50-3(3.5569),328.50+3(3.5569))

=(317.83, 339.17)

If mean is shifted to 330 new conf interval

( 330-3(3.5569),330+3(3.5569))

=(319.33, 340.67)

340.67-339.17 = 1.50

Thus proportion of non conforming units will be nil as there is no reading between 340.67 and 339.17