A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 7% rate of defects, what is the probability that this whole shipment will be accepted

Question

anonymous · Answer

please help EMERGENCY!!!!!!! TIMED EXAM

paxpolaris · Answer

so if you take a sample of 30 ... you want either 0, 1, or 2 defective pieces

anonymous · Answer

I DONT UNDERSTAND

paxpolaris · Answer

you have a huge shipment (assume infinite) with 7 percent defective pieces.

paxpolaris · Answer

you  take a sample of 30 pieces.. if 3 or more pieces are defective you cannot accept it

paxpolaris · Answer

so when you are taking a sample of 30 pieces ... you only want to find less than 3 defectives ... that is either 0, 1, or 2.

paxpolaris · Answer

do you follow so far.

paxpolaris · Answer

?

anonymous · Answer

yes

anonymous · Answer

hello??????

paxpolaris · Answer

the probability of getting 0 defectives: $$(1-0.07)^{30}=(0.93)^{30}$$

paxpolaris · Answer

probability of 1 defective $$.93^{29}\times .07^1\times(_{30}C_1)$$

paxpolaris · Answer

probability of 2 defective :$$.93^{28}\times.07^2\times(_{30}C_2)$$