Answer :
We use the binomial distribution:
[tex]P _{a}= \sum^c_d_=_0 \frac{n!}{d!(n-d)!} p^d (1-p)^n^-^d[/tex]
In this formula, c is the acceptable number of defectives; n is the sample size; p is the fraction of defectives in the population. Our c is 2; n is 58; and p is 0.11. Once we evaluate that summation, we get 0.0388. This has a 3.88% chance of being accepted. Since this is such a low chance, we can expect many of the shipments like this to be rejected.
[tex]P _{a}= \sum^c_d_=_0 \frac{n!}{d!(n-d)!} p^d (1-p)^n^-^d[/tex]
In this formula, c is the acceptable number of defectives; n is the sample size; p is the fraction of defectives in the population. Our c is 2; n is 58; and p is 0.11. Once we evaluate that summation, we get 0.0388. This has a 3.88% chance of being accepted. Since this is such a low chance, we can expect many of the shipments like this to be rejected.