When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 48 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 3000 batteries, and 1% of them do not meet specifications.

a. What is the probability that this whole shipment will be accepted?

b. Will almost all such shipments be accepted, or will many be rejected?

a) the probability that this whole shipment will be accepted is 0.8731

b) Almost all shipments (87.31% of the shipments) would be accepted

Step-by-step explanation:

a) Given that:

p = 1% = 0.01

n = 48

Binomial probability states that

Addition rule for mutually exclusive events is:

P(A or B) = P(A) + P(B)

To get the probability that this whole shipment will be accepted we evaluate at x = 0, 1, 2

Using addition rule:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.6173 + 0.1848 + 0.071 = 0.8731

the probability that this whole shipment will be accepted is 0.8731

b) Almost all shipments (87.31% of the shipments) would be accepted

2nd one in the first row is correct