The time between customer arrivals at a furniture store has an approximate exponential distribution with mean $\theta = 8.5$ 8.5 minutes. If a customer just arrived, find the probability that the next customer will not arrive for at least 20 minutes.
A) 0.095089
B) 0.653770
C) 0.346230
D) 0.904911

Question

Quizplus · Accepted Answer

The probability that the next customer will not arrive for at least 20 minutes is given by the exponential distribution's survival function: $ P(X > 20) = e^{-20/\theta} $. Substituting $\theta = 8.5$, we get $ P(X > 20) = e^{-20/8.5} \approx 0.095089 $.

The Time Between Customer Arrivals at a Furniture Store Has θ=8.5\theta = 8.5θ=8.5

The Time Between Customer Arrivals at a Furniture Store Has $\theta = 8.5$