Chapter 4.2, Problem 43E

(a)

To determine

To calculate: The probability that a call will come within $\frac{1}{2}$ minute when the normal time between the inbound calls at a switchboard is $3$ minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:

$P\left(t\right)=1-e^{-\frac{t}{3}}$

(b)

To determine

To calculate: The probability that a call will come within $2$ minutes when the normal time between the inbound calls at a switchboard is $3$ minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:

$P\left(t\right)=1-e^{-\frac{t}{3}}$

(c)

To determine

To calculate: The probability that a call will come within $5$ minutes when the normal time between the inbound calls at a switchboard is $3$ minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:

$P\left(t\right)=1-e^{-\frac{t}{3}}$