Seismologists have discovered a thermal disturbance in a remote location near the polar ice caps.Since the disturbance appears to occur randomly, they model the event using an exponential random variable X.If the mean time between occurrences is 52.25 hours, what is the probability that there will be at least 24 hours between occurrences?
A) 0.0190
B) 0.3683
C) 1.000
D) 0.6317

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X > x) = e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}}$. Given the mean time between occurrences is 52.25 hours, $\lambda = \frac{1}{52.25}$. To find the probability that there will be at least 24 hours between occurrences, we calculate $P(X > 24) = e^{-\frac{24}{52.25}}$, which simplifies to approximately 0.6317.

Seismologists Have Discovered a Thermal Disturbance in a Remote Location