Respuesta :
The manufacturer took a sample of 90 and found 2 defective.
This implies that there will always be 2 defective parts in any 90 parts chosen.
If they make 13770 parts every day (i.e. the mean production capacity), then the expected number of defective parts must be:
[tex]\begin{gathered} E(X)=P(X)\times\mu \\ P(X)=\text{probability of event X} \\ \mu=\text{average value} \\ E(X)=\text{Expected value} \end{gathered}[/tex]If we take event X as the event of finding a defective part,
We can therefore calculate the expected number of defective parts using the formula above as:
[tex]\begin{gathered} E(X)=P(X)\times\mu \\ P(X)=\frac{2}{90} \\ \mu=13770 \\ E(X)=\frac{2}{90}\times13770 \\ \\ \therefore E(X)=30.444\approx30\text{parts} \end{gathered}[/tex]Therefore, the expected number of defective parts is 30 parts per day
