2. If the lathe can be adjusted to have the mean of the lengths to any desired value, what should it

be adjusted to? Why?

We determined it should be adjusted to 1.0

Problem 7 is what I am having trouble with.

7. Now assume that the mean has been adjusted to the best value found in part 2 at a cost of $80. Calculate the reduction in standard deviation necessary to have 90%, 95% and 99% of the parts

My Answer

1.012 original mean

1.00 adjusted mean

P(.98 -1.00)

.98 -1.00 z equals 1.645 for a 90% confidence interval.

1.012 - 1.00 = 0.012 = 7.29

1.645 1.645

7.29² x $80.00 = 4,251.53

.98 -1.00 z equals 1.96 for a 95% confidence interval.

1.012 - 1.00 = 0.012 = 6.122

1.96 1.96

6.122² x 80.00 = $2,998.31

1.96 1.96

.98 -1.00 z equals 2.57 for a 99% confidence interval.

1.012 - 1.00 = 0.012 =4.669

2.57 2.57

4.669² x 80.00 = 1,743.96