Question

Jefferson informatics provides tactical support over there phone. calls arrive every 20 seconds on average. assuming the distribution of times between calls is exponential, what is there probability that the next call comes in under 25 seconds?

a. 0.39
b. 0.49
c. 0.61
d. 0.76

Answer 1

The probability that the next call comes in under 25 seconds is approximately 0.39.

Step-by-step explanation:

The distribution of times between calls is exponential with an average rate of one call every 20 seconds. The probability that the next call comes in under 25 seconds can be calculated using the cumulative distribution function for the exponential distribution. The cumulative distribution function is given by P(T < t) = 1 - e^(-λt), where λ is the rate parameter and t is the time interval.

In this case, λ = 1/20 and t = 25 seconds (or 25/60 minutes). Plugging in these values, we get P(T < 25/60) = 1 - e^(-(1/20)(25/60)) ≈ 0.39.

Therefore, the probability that the next call comes in under 25 seconds is approximately 0.39.