# Find probability that a gap greater than 7 seconds occurs between two consecutive arrivals

So I have a question that basically says: Customers arrive at a facility at a mean rate of $$12$$ per minute. Find the Probability that a gap of greater than $$7$$ seconds occurs between two consecutive arrivals.

I've started the question and found the mean time between arrivals ($$\frac{1}{12}$$ minutes $$= 5$$ seconds). I also know I need to use the negative exponential distribution, I should use $$e^{-λt}$$, however, I'm not sure what my $$\lambda$$ and t value should be. I think it might be quite simple and I'm overthinking it, any help on how I would obtain $$\lambda$$ and t would be great.

If your time was in unit of minutes, your $$\lambda$$ would be $$1/12$$, but it is not, right, it is more convenient for us to use seconds and use $$\lambda = 0.2$$ per second. Then we use the cumulative distribudion function to find the probability of being outside the interval $$[0, 7]$$ seconds. So we may take $$1 -$$P(being in that interval).
The CDF of $$\lambda e^{- \lambda t}$$ is $$1 - e^{-\lambda t}$$.
This equals $$1 - CDF[7]$$ with the right $$\lambda$$ (rate, intensity).
$$1 - CDF[7] = 1 - (1 - e^{-\lambda 7} )= e^{-0.2*7} = 0.247$$