The time between calls to an emergency 911-call center is exponentially distributed with a mean time between calls of 645 seconds. Based on this information, what is the probability that the time between the next two calls is between 200 and 400 seconds?
A) Approximately 0.47
B) About 0.199
C) About 0.747
D) About 0.801

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X \leq x) = 1 - e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}}$. For a mean of 645 seconds, $\lambda = \frac{1}{645}$. To find the probability that the time between calls is between 200 and 400 seconds, we calculate $P(200 < X < 400) = P(X < 400) - P(X < 200)$. Substituting the values, we get approximately 0.199.

The Time Between Calls to an Emergency 911-Call Center Is