Question 1204105
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I'd like to make some comments after the solution by @Theo.


As @Theo shown in his post, the test accepts almost all shipments  ($99.31%)
and rejects very few shipments  (%0.69).


It means that the test is not adequate and does not perform its functions properly.



                            It is not surprising.



It is obvious that in order for the test works adequately,  it must recognize  2%  of the control size.


If three defective batteries are admitted in the shipment,  it means that the size of the control set
must be about   {{{3/0.02}}} = 150 batteries.


With the control size of  38  batteries,  3 defective batteries make the gap of   {{{3/38}}} = 0.079 = 7.8%,
which is too wide and admits  (passes)  too many defective shipments.



            It is what a person,  who solves this problem, 

            should understand after completing the solution.