SOLUTION: Errors in a billing process often lead to customer dissatisfaction and ultimately hurt bottom-line profits. An article in Quality Progress discussed a company where 40% of the bill
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Question 587324: Errors in a billing process often lead to customer dissatisfaction and ultimately hurt bottom-line profits. An article in Quality Progress discussed a company where 40% of the bills prepared contained errors. If 10 bills are processed,what is the probability that
a. 0 bills will contain errors?
b. exactly 1 bill will contain an error?
c. 2 or more bills will contain errors?
d. What are the mean and the standard deviation of the probability distribution?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where 
is the probability of success on any given trial is given by:
\ =\ {n \choose k}\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where 
is the number of combinations of things taken at a time and is calculated by !})
Part a)
\ =\ {10 \choose 0}\left(0.4\right)^0\left(0.6\right)^{10})
Part b)
\ =\ {10 \choose 1}\left(0.4\right)^1\left(0.6\right)^{9})
Computation Hints:
Part c)
\ =\ \sum_{i\,=\,2}^{10}{10 \choose i}\left(0.4\right)^i\left(0.6\right)^{10\,-\,i})
Which is a computational nightmare but fortunately it is the same as:
\ =\ 1\ -\ P_{10}\left(\leq1,0.4\right)\ =\ 1\ -\ \sum_{i\,=\,0}^{1}{10 \choose i}\left(0.4\right)^i\left(0.6\right)^{10\,-\,i})
and since
\ =\ \sum_{i\,=\,0}^{1}{10 \choose i}\left(0.4\right)^i\left(0.6\right)^{10\,-\,i})
is simply the sum of the answers to Part a) and Part b), the answer to Part c is found by adding the answer to a) to the answer to b) and then subtracting the sum from 1.
Part d)
The mean of a binomial distribution is 
. For this problem, 
The variance of a binomial distribution is )
. For this problem: )
The standard deviation is the positive square root of the variance.
John
My calculator said it, I believe it, that settles it
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