#### Question

the billing department of a major credit card company attempts to control errors on customers billa. Suppose that occur according to a poisson distribution with a parameter. what is the probability that a customers bill selected at random will contain one error?

Verified

#### Step 1

1 of 2

Formula $\textbf{Poisson probability}$:

$P(X=k)=\dfrac{\lambda^k e^{-\lambda}}{k!}$

The errors occur according a Poisson distribution with some parameter $\lambda$.

The probability that a customers bill selected at random will contain one error is then the formula of Poisson probability evaluated at $k=1$.

$P(X=1)=\dfrac{\lambda^1 e^{-\lambda}}{1!}=\dfrac{\lambda e^{-\lambda}}{1}=\lambda e^{-\lambda}$

## Create an account to view solutions

#### Probability and Statistics for Engineers and Scientists

9th EditionKeying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers
1,203 solutions

#### Statistics for Business and Economics

11th EditionDavid R. Anderson, Dennis J. Sweeney, Thomas A. Williams
2,223 solutions

#### The Practice of Statistics for the AP Exam

5th EditionDaniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor
2,433 solutions

#### Statistics and Probability with Applications

3rd EditionDaren S. Starnes, Josh Tabor
2,555 solutions