Question

I need help on how to calculate this correctly

When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test

4040

batteries and determine whether each is within specifications. The entire shipment is accepted if at most

33

batteries do not meet specifications. A shipment contains

60006000

​batteries, and

22​%

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?

Answer 1

Given : n = 40 , p = 0.02 , q = 0.98

x be the number of batteries do not meet specifications.

x follows binomial distribution with n = 40 and p = 0.02

P( x ≤ 3 )

=BINOM.DIST(3,40,0.02,TRUE)

= 0.9918

The probability that this whole shipment will be​ accepted is 0.9918

Almost all such shipments be​ accepted

99.18% shipments be​ accepted and 0.82% will be rejected.