Question

A sample of Coke bottles has a mean value of 12.19 oz. & a standard deviation of 0.11 oz. A sample bottle is taken from the production line and found to contain 11.80 oz. Should the quality control analyst be concerned the machine is underfilling the bottles? (In other words, using the range rule of thumb, does 11.80 oz. represent an unusually low amount?)

Answer 1

from range rule of thumb:

lower usual value =mean-2*standard deviation =12.19-2*0.11 =11.97

and upper usual value =mean+2*standard deviation =12.19+2*0.11 =12.41

since value 11.80 falls outside the region of usual values, quality control analyst should be concerned that the machine is underfilling.