$($Please solve using Minitab$)$

A company producing special screws specified that the lengths have to be in the range of $125$cm $\backslash$pm $0\mathrm{.}25$cm$.$ During the process of production monitoring, control charts were kept for controlling such specified measures and all output was inspected against specification limits$.$ The sales team requested tighter limits$,$ prompting the question of whether the limits could be reduced to $\backslash$pm $0\mathrm{.}15$cm$,$ as this could result in significant orders from a new customer who preferred these limits$.$ The production supervisor wants to use a control chart data to draw a histogram and check if it fits a normal distribution $($based on the shown samples$),$ then calculate Cpk$,$ across samples from a week's work, to obtained information on the process capability.

Could the limits be reduced as requested? Explain your analysis.