Question 1084335
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.


<a href = "http://stattrek.com/online-calculator/binomial.aspx" target = "_blank">http://stattrek.com/online-calculator/binomial.aspx</a>


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


<img src = "http://theo.x10hosting.com/2017/061101.jpg" alt="$$$" </>


my inputs were in the first 3 boxes.


the calculator gave me the rest.