Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order?
A) $f ( x ) = \frac { 1 } { 5 } e ^ { - \frac { x } { 5 } }$
B) $f ( x ) = \frac { 1 } { 3 } e ^ { - \frac { x } { 3 } }$
C) $f ( x ) = \frac { 2 } { 3 } e ^ { - \frac { 2 } { 3 } x }$
D)None of these are correct.

Question

Quizplus · Accepted Answer

The probability density function for an exponentially distributed random variable with mean $\mu$ is $f(x) = \frac{1}{\mu} e^{-\frac{x}{\mu}}$. Given the mean is 1.5 minutes, the correct function is $f(x) = \frac{2}{3} e^{-\frac{2}{3}x}$.

Fast Food Restaurants Pride Themselves in Being Able to Fill f(x)=15e−x5f ( x ) = \frac { 1 } { 5 } e ^ { - \frac { x } { 5 } }f(x)=51​e−5x​

Fast Food Restaurants Pride Themselves in Being Able to Fill $f ( x ) = \frac { 1 } { 5 } e ^ { - \frac { x } { 5 } }$