When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 49 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 6000 batteries, and 1% 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?
Accepted Solution
A:
Answer:Step-by-step explanation:Given that A shipment contains 6000 batteries, and 1% of them do not meet specifications.Sample size =49 If x is the number of batteries not meeting specifications then x is binomial with n =49 and p = 0.01Because i) each toy is independent of the otherii) There are only two outcomesProbability whole shipment is accepted = Prob (X≤3)=0.9885Hence almost all shipments would be accepted.