possible
This question: 1
point(s) possible
Submit quiz
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly sele and test 45 batteries and determine whether each is within specifications. The entire shipment is accepted if at $\mathrm{mo}$ 2 batteries do not meet specifications. A shipment contains 4000 batteries, and $2 \%$ of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Answer
Final Answer: The probability that this whole shipment will be accepted is approximately \(\boxed{0.939}\). This means that almost all such shipments will be accepted.
Step 1 ：The problem is asking for the probability that a shipment will be accepted given that 2% of the batteries do not meet specifications. This is a binomial distribution problem where we are selecting 45 batteries and we want to know the probability that at most 2 of them do not meet specifications. The probability of a battery not meeting specifications is 0.02.
Step 2 ：Let's denote the number of batteries as \(n = 45\) and the probability of a battery not meeting specifications as \(p = 0.02\).
Step 3 ：Using these values, we can calculate the probability of the shipment being accepted.
Step 4 ：The calculated probability is approximately 0.939.
Step 5 ：Final Answer: The probability that this whole shipment will be accepted is approximately \(\boxed{0.939}\). This means that almost all such shipments will be accepted.
