Question

The design diameter of a cylinder is 60 mm (millimeters). A manufacturing process can make them according to a Normal distribution with mean 60 and standard deviation 0.1

When the process is in control, if samples of size 12 were taken, the sample means will have a standard deviation of _____ mm

(provide three decimal places)

The design diameter of a cylinder is 60 mm (millimeters). A manufacturing process can make them according to a Normal distribution with mean 60 and standard deviation 0.1

When the process is in control, if samples of size 12 were taken, the control limits for the sample means should be 60 +/- ______ (so that 99.7% of the sample means would be within those limits)

(provide three decimal places)

Consider the data in "spc example.xlsx". In it, samples of size 10 are taken at various times during day, and weights recorded. For the first sample, what is the sample average?

Answer 1

we have diameter of cylinder ( X) has normally distributed with mean = 60 mm and standard deviation = 0.1 mm

Here sample size n= 12 is taken so sample mean ( X bar ) has standard deviation of  /√n = 0.1/√12

So sample mean will have standard deviation of 0.029 mm

2) The process is in control the control limits for the sample mean should be xbar +/- 3 * (/√n)

60 +/- 3* 0.029

60 +/- 0.087