Question

A manufacturer took a random sample of 90 parts that were made by a particularmachine and found that 2 of those parts were defective. If the machine produces13,770 parts every day, estimate the number of defective parts the machine willproduce per day.

Answer 1

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:

`\begin{gathered} E(X)=P(X)*\mu \\ P(X)=\text{probability of event X} \\ \mu=\text{average value} \\ E(X)=\text{Expected value} \end{gathered}`

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:

`\begin{gathered} E(X)=P(X)*\mu \\ P(X)=(2)/(90) \\ \mu=13770 \\ E(X)=(2)/(90)*13770 \\ \\ \therefore E(X)=30.444\approx30\text{parts} \end{gathered}`

Therefore, the expected number of defective parts is 30 parts per day