Question 331840: Among a shipment of 5,000 tires, 1,000 are slightly blemished. If one purchases 10 of these tires, what is the probability that 3 or less (P (x <= 3) are blemished?
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! Among a shipment of 5,000 tires, 1,000 are slightly blemished. If one purchases 10 of these tires, what is the probability that 3 or less (P (x <= 3) are blemished?
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let X=number of blemished tires
This is a hypergeometric problem
\ =\ \sum_{i=0}^3\left(1000\cr i\right)\left(4000\cr 10-i\right)\div{\left(5000\cr 10\right)})
Time consuming and messy to compute, but since N=5000 is much greater than n=10, we can use the binomial approximation, with prob of blemish p=1000/5000=0.2 and sample size n=10
\ =\ \sum_{i=0}^3\left(10\cr i\right\)(0.2)^i(0.8)^{10\,-\,i}\ =0.879)
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