Question

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?

Answer 1

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%.