Suppose that a single sampling plan with $n=50$ and $c=1$ is being used for receiving inspection where the supplier ships the product in lots of size $N=500.$ For a process average $($i$.$e$.,$ percent nonconforming$)$ of $0\mathrm{.}4\%$ and assuming rectifying inspection, compute

$($a$)$ the probability of acceptance,

$($b$)$ the average outgoing quality, and

$($c$)$ the average total number of units inspected.