Question 1039790: Need some help with this question please! I know I have to know 0.9 is what isn't defective for (a) and 0.85 for (b), but from there I am lost.
A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 17 randomly selected pens yields no more than two defective pens.
(a) Find the probability that this shipment is accepted if 10% of the total shipment is defective.
(b) Find the probability that this shipment is not accepted if 15% of the total shipment is defective.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Probability there are 0=0.9^17=0.1668
there is 1= 17*.9^16*.1, which is 17C1(0,9)^16*(0.1)^1=0.3150
there are 2=17C2(0.9)^15(0.1)^2=0.2800; 17C2= 17*16/2=136
The probability is their sum, or 0.7618.
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Analogous for 0.85
.85^17=0.0631
17(.85^16)(.15^1)=0.1893
136*(.85^15)(.15^2)=0.2673
This sum is 0.5197. It is less, as it should be because there is a higher probability of defective pens and 0,1,2 defects will have a lower probability.
it is nCk(p)^(n-k)*(1-p)^k
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