Question

When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 51 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 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. ​(Round to four decimal places as​ needed.) The company will accept nothing​% of the shipments and will reject nothing​% of the​ shipments, so many of the shipments will be rejected. almost all of the shipments will be accepted. many of the shipments will be rejected. ​(Round to two decimal places as​ needed.)

Answer 1

Answer:

Here, n = 51

Probability of success, p = 0.02

Probability of failure, q = 0.98 (= 1−0.2)

The entire shipment is accepted if at most 2 batteries do not meet specification. That is we have to find P(x ≤ 2).

probability = P(x=0)+p(x+1)+p(x=2)

=(0.02)^0(0.98)^51-0+(0.02)^1(0.98)^51-1+(0.02)^2(0.98)^51-2.

= 0.0071 +0.0073+0.00015

= 0.0145

= 1.45%