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

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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.