# inter arrival time ( continuous exponential distribution)

The customers arrive at store with exponentially distributed interarrival times with a mean of 30 minutes. What is the probability that interarrival time between two successive customers is 2 hours or more?

My attempt: 2 customers arrive every hour, therefore λ=2.

P(T≥2)=∫ λ^(-λt) dt ( where $λ=2$, upperbound is infinity, and lowerbound is 2).This gives an answer of=$0.018$

however the answer in the answer key is $0.18$ can someone tell me what I did wrong. Thank you very much

The CDF of exponential distribution is $F_T(t)=1-e^{-\lambda t}$. If described in the unit of hours, we have $\lambda^{-1}=0.5$ and $\lambda=2$. The question asks for $\Pr(T>2)$ which is given by $1-F_T(2)$ or $e^{(-2)(2)}=0.018$, and your answer is correct.