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, what is the probability that the time between any two cars arriving will exceed 11 seconds?
A) Approximately 1.0
B) Approximately 0.48
C) About 0.52
D) About 0.75

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X > x) = e^{-\lambda x}$, where $\lambda$ is the rate parameter (4 cars per minute in this case), and $x$ is the time. To find the probability that the time exceeds 11 seconds, we first convert 11 seconds to minutes (11/60 minutes) since $\lambda$ is in cars per minute. Then, we substitute $\lambda = 4$ and $x = 11/60$ into the formula: $P(X > 11/60) = e^{-4 \times 11/60} \approx 0.48$.

The Transportation Manager for the State of New Jersey Has