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home / study / math / statistics and probability / questions and answers / a stationary store has decided to accept a large ... Question A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 15 randomly selected pens yields no more than two defective pens. (a) Find the probability that this shipment is accepted if 5% of the total shipment is defective. (Use 3 decimal places.) (b) Find the probability that this shipment is not accepted if 15% of the total shipment is defective. (Use 3 decimal places.)

Explanation / Answer

Here the problem follows a binomial distribution so we take as follows:

a)x is bin(20, 0.05)
P[shipment accepted] = P[x<=2]
= 0.95^20 + 20c1*0.05*0.95^19 + 20c2*0.05^2*0.95^18 = 0.9245

b)
x is bin(20,0.15)
P[shipment NOT accepted] = P[x>2] = 1 - P[x<=2] computed in the same way
= 1 - 0.4049 = 0.5951

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