Question

Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution.

Find the probability that a call takes:
(a) 3 minutes or less.
(b) 4 minutes or less.
(c) 5 minutes or less.
(d) longer than 5 minutes.

Answer 1

Explanation:

Let X be the time for any customer to call at any time to make reservation in Nite Time Inn.

Given that X is exponential with mean = 4 minutes

We are to find the probability

(a) 3 minutes or less.

=
`P(X\leq 3)=1-e^(-3/4) =0.5276`

(b) 4 minutes or less.

`=P(X\leq 4)\\=1-e^(-4/4) =0.6321`

(c) 5 minutes or less.

`=P(X\leq 5)\\=1-e^(-5/4) =0.7135`

(d) longer than 5 minutes.

=1-P(X≤5) = 0.2865