Hello, not sure if the "expert answer" is correct. Either way, please explain thoroughly. Thank you so much!

Problem 4 A process that produces titanium forgings for automobile turbocharger wheels is to be controlled through use of a x-bar chart. Initially, 100 samples of size 4 are collected, and a 3-sigma control chart is setup to monitor the process: UCL=12, CL=10, LCL=8. If the process average suddenly shifted to 11, what is that probability that the shift will be detected on the second sample following the shift? Expert answer S Expert in Statistics and Probability o=(12-10)/3, since x(bar)+3*=UCL, 6=2/3 therefore, the probability of shift will be detected on second sample is 1-(4((12-11)/2/3)-4((8-11)/2/3)), here 4() is the cdf function of SN variate and can be calculated fron table, therefore required probability= 1-0.933 =0.068