SOLUTION: 1 in every 2000 automobiles produced has a particular manufacturing defect. Use a binomial distribution to find the probability of finding 4 cars with the defect in in a random s

Question 1084335: 1 in every 2000 automobiles produced has a particular manufacturing defect. Use a binomial distribution to find the probability of finding 4 cars with the defect in in a random sample of 6500 cars.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
binomial distribution is:

p(x) = p^x * q^(n-x) * c(n,x)

p = 1/2000

this is the probability that any car picked at random from the population will be defective.

q = 1 minus p = 1999/2000

this is the probability that any car picked at random from the population will not be defective.

p(x) is the probability that exactly x cars will be defective.

n is the number of cars in the sample.

when x = 4 and n = 6500, the binomial distribution formula becomes:

when x = 4, (n-x) = (6500-4) = 6496.

the formula of p(x) = p^x * q^(n-x) * c(n,x) becomes:

p(4) = (1/2000)^4 * (1999/2000)^6496 * c(6500,4) = .1802934715

this has been confirmed to be correct through the use of the following binomial calculator.

http://stattrek.com/online-calculator/binomial.aspx

here's a picture of my inputs and the outputs from the calculator.

$$$

my inputs were in the first 3 boxes.

the calculator gave me the rest.

RELATED QUESTIONS
An automobile manufacturer finds that 1 in every 2000 automobiles produced has a... (answered by Boreal)

PROBABILITY DISTRIBUTIONS (Binomial and Poisson) ABC company estimates the net profit... (answered by richard1234)

For a critical defect, the sampling plan is n = 1,200 and accept/reject = 0/1. If the... (answered by ewatrrr)

7. Ten percent of the tools produced in a certain manufacturing process turn out to be... (answered by ewatrrr)

The cost in millions of dollars for a company to manufacture x thousand automobiles is... (answered by oscargut)

A manufacturing machine has a 1% defect rate. If 4 items are chosen at random, what is (answered by ewatrrr)

A manufacturing machine has a 1% defect rate. If 9 items are chosen at random, what is (answered by ikleyn)

how would u solve this prob, A map has a scale of 1 in: 15 miles. Use the map given... (answered by rfer)

A quality control inspector has found that 3.2% of the garments produced at Standard... (answered by Fombitz)