Show that in Prob. 1, the requirement of the significance level = 0.3% leads to LCL

Show that in Prob. 1, the requirement of the significance level α = 0.3% leads to LCL = μ - 3σ/√n and UCL = μ + 3σ/√n, and find the corresponding numeric values.

Data from Prob. 1

Suppose a machine for filling cans with lubricating oil is set so that it will generate fillings which form a normal population with mean 1 gal and standard deviation 0.02 gal. Set up a control chart of the type shown in Fig. 537 for controlling the mean, that is, find LCL and UCL, assuming that the sample size is 4.