Question

The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is _________.
\text{[round off to 3 decimal places]}

Hint:

For exponential distributions, the probability that the time exceeds a certain value is given by \( P(T>t) = e^{-t/\tau} \).

Answer 1

Correct Answer: 0.365

The exponential distribution is given by: \[ P(T>t) = e^{-t/\tau}, \] where \( \tau = 15 \, \text{minutes} \) is the mean time. The probability that the passenger will miss the flight is the probability that the time exceeds 15 minutes: \[ P(T>15) = e^{-15/15} = e^{-1} \approx 0.3679. \] Thus, the probability that the passenger will miss the flight is approximately \( 0.368 \).