>I'm confused as to the meaning there. What is it about phone calls that follow an exponential distribution?

Sorry for the confusion. Lemme clarify a bit. Say you work at an office. 9am to 5pm. 8 hours a day.

scala> 60x60x8

res45: Int = 28800

So a phone call can arrive in any one of those 28,800 seconds. Putting it another way, the probability p of getting a phone call at any particular second is very remote, but the number of seconds aka trials is n=28800 ie. very large. Anytime you have very small p and very large n, that's a nice candidate for a particular member of the exponential family of distributions. In this case, the arrival times of phone calls to your office will be Poisson.

Say you hire an office assistant to count the number of phone calls every day, and she tells you after a month that your office averages say 24 calls a day. That 24 is your mu, the mean of the Poison distribution.At that point you know everything you need to know about the distribution, because Poisson is a discrete distribution whose probability p is specified entirely by the mean mu!

So you can go off and compute the probability p like so:

scala> import scala.math.{exp,pow}

scala> def fact(n:Int):Int = { if( n>1) nfact(n-1) else 1}

scala> def p(mu:Int,n:Int) = {pow(mu,n)exp(-mu)/fact(n)}

The chances of your office getting 4 or fewer phone calls by noon is then easy to figure out. Since you average 24 calls in 8 hours, you should average 9 calls by noon. So the probability of getting 4 or fewer calls would be

scala> (0 to 4).map(p(9,_)).sum

res46: Double = 0.05496364149510491

So you have a 5% chance of getting 4 or fewer calls by noon. If someone offers to bet a million dollars that your office will get 4 or fewer calls by noon, the odds of winning that bet are 1 in 19.

edit:formatted for better readability.