54.8k views
0 votes
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.

1 Answer

5 votes

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

User MatsT
by
6.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.