Question

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 6000 ​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? The probability that this whole shipment will be accepted is nothing

Answer 1

Distribution: Hypergeometric distribution

Formula: P(X =k) =C(K, k)*C(N-K, n-k)/C(N, n)

Where,

P =Probability;

X =Hypergeometric random variable;

N =Population size =6000;

n =Sample size =48;

K =Number of successes (do not meet specifications) in population =6000*2% =120;

k =number of required successes in sample =at most 2.

The probability that this whole shipment will be​ accepted =P(k 2) =P(k =0)+P(k=1)+P(k=2) =0.9295

So, almost all such shipments will be​ accepted.