$6.$ The current steel rod production process has the length of a rod at $218$ in $+/-1\mathrm{.}6$ in$.$ The company is closing a deal with a new high$-$volume customer who expects consistent quality. You suspect that the process does not always meet specifications. You bring the issue to the CEO who is willing to invest in improving the process capability. The Chief Engineer, however, claims that the process is working well, and no improvements are necessary. You measure the lengths of $15$ consecutive rods produced by the process. The measurements are given below. Use the process capability index method $($k$=3)$ to determine if the process meets specifications consistently. Please show your work.