A quality analyst wants to construct a control chart for determining whether four machines, all producing the same product, are in control with regard to a particular quality attribute. Accordingly, she inspected $1,000$ units of output from each machine in random samples, with the following results:

Machine Total Defectives

#$123$

#$215$

#$329$

#$413$

What is the estimate of the standard deviation of the sampling distribution of sample proportions for this process?

Multiple Choice

$\mathrm{.}00002$

$\mathrm{.}00016$

$\mathrm{.}016$

$\mathrm{.}0044$

$\mathrm{.}04$