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]}
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]}
\text{[round off to 3 decimal places]}
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For exponential distributions, the probability that the time exceeds a certain value is given by \( P(T>t) = e^{-t/\tau} \).
Updated On: Dec 26, 2025
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Verified By Collegedunia
Correct Answer: 0.365
Solution and Explanation
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 \( 0.368 \).
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