Question

Industrial quality control programs often include inspection of incoming materials from suppliers. If parts are purchased in large lots, a typical plan might be to select 20 parts at random from a lot and inspect them. A lot might be judged acceptable if one or fewer defective parts are found among those inspected. Otherwise, the lot is rejected and returned to the supplier.
Find the probability of accepting lots that have the given percentage of defective parts. (Round your answers to three decimal places.)
(Hint: Identify success with a defective part.)

(a) 5% defective parts
P(lot will be accepted) =

(b) 15% defective parts
P(lot will be accepted) =

(c) 20% defective parts
P(lot will be accepted) =

Answer 1

Answer:

Step-by-step explanation:

Given that industrial quality control programs often include inspection of incoming materials from suppliers. If parts are purchased in large lots, a typical plan might be to select 20 parts at random from a lot and inspect them.

A lot might be judged acceptable if one or fewer defective parts are found among those inspected. Otherwise, the lot is rejected and returned to the supplier.

No of defectives in the lot would be binomial with constant p probability for being defective.  There are only two outcomes

a) 5% defective parts Here p = 0.05

P(lot will be accepted) =

$P(X\leq 1)$

=0.7358

b) p = 0.15

$P(X\leq 1)\\\\=0.1756$

c)  p=0.20

$P(X\leq 1)\\\\=0.06912$