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.

Answer 1

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.