53.1k views
2 votes
The time between calls is exponentially distributed with a mean time between calls of 10 minutes.

What is the probability that the time until the first call is less than five minutes?

1 Answer

5 votes

Final answer:

The probability is approximately 0.3935 or 39.35%.

Step-by-step explanation:

To find the probability that the time until the first call is less than five minutes, we can use the cumulative distribution function for exponential distribution. Let T be the time elapsed between calls. The mean time between calls is 10 minutes, so the rate parameter λ = 1/10. The cumulative distribution function is P(T < t) = 1 - e^(-λt). Plugging in t = 5 minutes, we have P(T < 5) = 1 - e^(-1/2) ≈ 0.3935. Therefore, the probability that the time until the first call is less than five minutes is approximately 0.3935, or 39.35%.

User Andy Whitfield
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories