Please help!

#1
I don’t even know where to begin. Thank you in advance.

Suppose there are 500 items in the lot and their manufacturer claims that no more than 5% are defective. When the shipment is received at an assembly plant, a quality control manager asks his staff to take a random sample of size 20 from it without replacement and will accept the lot if there are at most 1 defective item in the sample. If let say 5% are defective in the entire lot, then it consists of 25 defective items. What is the probably that the manager will accept the lot?
 
Last edited:

staassis

Active Member
#2
Let X be the number of defective items in the 20-item sample.

Prob(accepting the lot) = Prob(X = 0) + Prob(X = 1).

Now

Prob(X = 0) = Prob(the 1st sampled item is not defective) * Prob(the 2nd sampled item is not defective | the 1st sampled item is not defective) * ...

Continue this logic.
 
#3
Let X be the number of defective items in the 20-item sample.

Prob(accepting the lot) = Prob(X = 0) + Prob(X = 1).

Now

Prob(X = 0) = Prob(the 1st sampled item is not defective) * Prob(the 2nd sampled item is not defective | the 1st sampled item is not defective) * ...

Continue this logic.
Thank you!!!!