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

Question

Quizplus · Accepted Answer

The exponential distribution is defined by the probability density function f(x|θ) = (1/θ) * e^(-x/θ). The probability that the time until the next event is at least t is given by P(X ≥ t) = e^(-t/θ). Here, θ = 8.5 and t = 20, so P(X ≥ 20) = e^(-20/8.5) ≈ 0.095089.

The Time Between Customer Arrivals at a Furniture Store Has