Question

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

Answer 1

Answer:

$\left \{ {{0.667 e^{-0.6667 x}, x \geq 0} \atop {0, x < 0}} \right$

Step-by-step explanation:

The probability density function for the exponential distribution is:

$\left \{ {{\mu e^{-\mu x}, x \geq 0} \atop {0, x < 0}} \right$

In which $\mu = \frac{1}{m}$ is the decay parameter and m is the mean.

It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes.

This means that $m = 1.5, \mu = \frac{1}{1.5} = 0.6667$

So, the answer is:

$\left \{ {{0.667 e^{-0.6667 x}, x \geq 0} \atop {0, x < 0}} \right$