A new car was put into production. It involved many assembly tasks. Each car was

Question

A new car was put into production. It involved many assembly tasks. Each car was inspected at the end of the assembly line and the number of defects per unit was recorded. For the first 100 cars produced, there were 40 defective cars. Some of the cars had no defects, a few had one defect, and so on. The distribution of defects followed a Poisson distribution. Based on the first 100 cars produced, about how many out of every 1,000 cars assembled should have one or more defects? About 660 About 165 About 630 About 330

Explanation / Answer

Let us first define two random variables

X: Number of defects in a car X~Poisson(lambda) lambda is unknown

Y: Number of defective cars out if n cars Y`Binomial(n,p) n is known.p is unkniwn.

p=P(a car is defective)=P(X>0)=1-exp(-lambda)

p_hat=1-exp(-lambda_hat)

here,p_hat=40/100=.4

so,labda_hat=.5108256

X~Poisson(.5108256)

so there should be 400 defective cars

may be the options are not correct or the problem is not stated clearly

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