Question 910769: A salesman found that in a shipment of 200 Smart TVs, 6.2% of Smart TV of a certain type are defective. Let the random variable X represent the number of defective Smart TVs, of the same brand, in a shipment. Suppose you wish to find the probability that X = 8. Does the random variable have a binomial or poisson distribution. How can you tell. If X is binomial distribution, would it be reasonable to use the poisson approximation? If not, why not? Solve the problem to arrive at answer for P(X=8)
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! It is important to keep in mind that the Poisson approximation to the binomial distribution works well
only when n is large and p is small.
In general, the approximation works well if:
n ≥ 20 and p ≤ 0.05, or if n ≥ 100 and p ≤ 0.10.
so.. Yes, it be reasonable to use the Poisson approximation.
Testing:
P(8) = poissonpdf(12.4, 8) = 0.0571
P(x=8) = binomcpdf(200,.062,8)=0.0554
Poisson a good approxiamation
Wish You the Best in your Studies.
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