Answer:
[tex]\left \{ {{0.667 e^{-0.6667 x}, x \geq 0} \atop {0, x < 0}} \right[/tex]
Step-by-step explanation:
The probability density function for the exponential distribution is:
[tex]\left \{ {{\mu e^{-\mu x}, x \geq 0} \atop {0, x < 0}} \right[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] 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 [tex]m = 1.5, \mu = \frac{1}{1.5} = 0.6667[/tex]
So, the answer is:
[tex]\left \{ {{0.667 e^{-0.6667 x}, x \geq 0} \atop {0, x < 0}} \right[/tex]
