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

question 22

Multiple Choice

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.

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Definitions:

Parasympathetic Nervous System

A division of the autonomic nervous system responsible for conserving energy and promoting a state of calmness and rest.

Acetylcholine

A neurotransmitter in both the central and peripheral nervous systems that plays an important role in muscle activation, memory, and learning.

Norepinephrine

A neurotransmitter and hormone involved in the body's fight or flight response, affecting heart rate, blood pressure, and blood glucose levels.

Epinephrine

Epinephrine, also known as adrenaline, is a hormone and neurotransmitter that increases heart rate, contracts blood vessels, and opens airways in response to stress or excitement.