defect An automobile manufacturer finds that 1 in every 2000 automobiles produce
ID: 2908160 • Letter: D
Question
defect An automobile manufacturer finds that 1 in every 2000 automobiles produced has a particular manufacturing efect in a random sample of 4500 cars (a) Use a binomial distribution to find the probability of finding 4 cars with the d b) The Poisson distrbution can be used to approximate the binomial distribution for large values of n and small values of p. Repeat (a) using a Poisson distribution and compare (a) The probablity using the binomial distribution is Round to five decimal places as needed ) b) The probability using the Poisson distribution is Round to ive decimal places as needed.) Compare the results. Choose the oorrect answer below O A. The probability caloulated using the binomial distribution is much larger O B. The probability caloulated using the Poisson distribution is much larger O C. The two probabilites are approximately the same.Explanation / Answer
Solution:-
(a) p = (4500C4)*(1/2000)^4*(1999/2000)^4496
= 17063165530125*(1/2000)^4*(1999/2000)^4496
= 0.11256
(b) np = 4500*(1/2000) = 2.25
That is the Poisson parameter For 4 cars
=> (e^(-2.25)*(2.25^4))/4!
= 0.11255
(C) option C. The two probabilites are approximataly the same.
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