a Rowans support desk receives calls throughout the day The

(a) Rowan’s support desk receives calls throughout the day. The time T(in minutes) between calls is modeled with an exponential distribution with mean 4.5. A call just arrived. What is the probability no call will be received in the next 5 minutes?

(b) 4.91

(c) 4.109

(d)4.110

Solution

a) T = the waiting time between 2 calls...

P [ T > 5 ] = 1 - P [ T <= 5 ] = 1 - [ 1 - e^-(4.5*5) ] = e^ (-22.5)

b) you meant mean= 4.5 or, waiting time=4.91??

if you meant mean=4.9...P [ T>5 ] = e^(-4.9*5) = e^(-24.5)..
and if you meant waiting time = 4.9...P [ T>4.9 ] = e^(- 4.5*4.9) = e^(-22.05)..