We have been given that in an assembly line, 56 out of 60 randomly selected parts have no faults. We are asked to predict the number of parts that will have no faults in a similar batch of 12,000 parts.
We will use proportions to solve our given problem.
[tex]\frac{\text{Not faulty parts}}{\text{Total parts}}=\frac{56}{60}[/tex]
[tex]\frac{\text{Not faulty parts}}{12,000}=\frac{56}{60}[/tex]
[tex]\frac{\text{Not faulty parts}}{12,000}\times 12,000=\frac{56}{60}\times 12,000[/tex]
[tex]\text{Not faulty parts}=56\times 200[/tex]
[tex]\text{Not faulty parts}=11,200[/tex]
Therefore, approximately [tex]11,200[/tex] parts will have no faults in a similar batch of 12,000 parts.
