The chair of the Quality Department at Motorola University wants to construct a p$-$chart for determining whether the four faculty members teaching the course are in a state of control concerning the number of students who fail in the course. Accordingly, the chair sampled $500$ final grades from last year for each instructor, and computed the number of failures per instructor as $13,11,0,$ and $16$ respectively. Compute the upper and lower standard control limits for this three sigma control chart.

Multiple Choice

$0\mathrm{.}0600$ and $0\mathrm{.}1400.$

$0\mathrm{.}9500$ and $0\mathrm{.}0500.$

$0\mathrm{.}0388$ and $0\mathrm{.}0012.$

None of the choices are correct.