Control charts for and R are maintained for an important quality characteristic. The sample size is n$=7$; and R are computed for each sample. After m$=35$ samples, we have found that:

a$)(15$ Points$)$ If the quality characteristic is normally distributed and if the specifications are $220\backslash$pm $35,$ what is the probability that the process meets the specifications?

b$)(25$ Points$)$ Calculate, Plot, and Comment on the process capability.