Question

Question Help When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 38 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 5000 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? The probability that this whole shipment will be accepted is I (Round to four decimal places as needed) The company will accept% of the shipments and will reject % of the shipments, so many of the shipments will be rejected. almost all of the shipments will be accepted

Answer 1

Sample size , n =    38
Probability of an event of interest, p =   0.01

P ( X = 0) = C (38,0) * 0.01^0 * ( 1 - 0.01)^38=      0.6826
P ( X = 1) = C (38,1) * 0.01^1 * ( 1 - 0.01)^37=      0.2620
P ( X = 2) = C (38,2) * 0.01^2 * ( 1 - 0.01)^36=      0.0490

P(accepeted) = P(X≤2) = P(X=0) + P(X=1) + P(X=2)= 0.9935

answer is order: 99.35%, 0.65%, almost all of the hipment will be accepted