Take a random sample of 1000 widgets from our line A quality

Take a random sample of 1000 widgets from our line. A quality rating was determined for each of the 1000 widgets, and the average quality rating in the sample was 4 with a standard deviation of 0.5. In addition, 6 of the 1000 widgets were found to be defective.

a) Estimate the average quality rating for widgets from our production line, and include the uncertainty in this estimate in the form, a ± b.

b) Estimate the proportion of widgets that are defective, and include the uncertainty in this estimate in the form, a ± b

Solution

a) here mean is 4 and SD(Xbar)=31.62

so a=4 b=3*31.62

b) here p=0.006 and sd(P)=0.002442

here a=0.006 and b=3*.002442