Question

A company purchases shipments of batteries and uses this acceptance sampling plan:  Randomly select and test 40 batteries.  Accept the batch if there are fewer than 3 defects.  A particular shipment of thousands of batteries has a 3.2% rate of defects. Below, we will find the probability that the whole shipment will be accepted.

1. What is the probability of success? Express as a probability, to three decimal positions:

2. What is the probability of failure?  Express as a probability, to three decimal positions:

3. Now let’s solve the problem. What is the probability that this whole shipment will be accepted? Round your answer to four decimal positions:  

4. Explain how you reached your answer, using at least one sentence. If you used a calculator function, which one did you use and what were your inputs?

Answer 1

1) probability of success =1-0.032=0.968 (probability that battery is ok)

2) probability of failure =0.032 (probability that battery is defective)

3) probability that this whole shipment will be accepted P(X<3)=P(X=0)+P(X=2)+P(X=3)=0.8644

4) ( use binomcdf function in ti-84 caculator : press 2nd -vars -binomcdf(40,0.03,2)