The transportation manager for the State of New Jersey has determined that the time between arrivals at a toll booth on the state's turnpike is exponentially distributed with λ = 4 cars per minute. Based on this information, the standard deviation for the time between arrivals is:
A) 25 seconds.
B) 3.87 seconds.
C) 15 seconds.
D) 2 minutes.

Question

Quizplus · Accepted Answer

The standard deviation for an exponential distribution is given by 1/λ, where λ is the rate parameter (4 cars per minute in this case). Since the rate is in cars per minute, the time between arrivals is in minutes per car. Therefore, the standard deviation is 1/4 minute per car, which is 0.25 minutes per car. Converting 0.25 minutes to seconds (0.25 * 60), we get 15 seconds.

The Transportation Manager for the State of New Jersey Has