$2.(20\%)$ Resistors are electronic circuits that are manufactured on a high$-$speed automated machine. To examine how the process is performing, six samples were taken, each containing three resistors.

Sample No X$1$ X$2$ X$3$

$199010011015$

$29959951010$

$3980981983$

$410249901007$

$5101310191004$

$699510101008$

$2.$a$.$ Does this process indicate variations from assignable causes? Show evidence to support your conclusion.

$2.$b$.$ You are given the following design specifications: Target Value $=1000,$ LSL $=980,$ USL $=1020.$ Are there any defective resistors among the samples? And how is this process compared to a world$-$class process of the same type? Show evidence to support your conclusion.