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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 :

Answer:

Step-by-step 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.

=[tex]P(X\leq 3)=1-e^{-3/4} =0.5276[/tex]

(b) 4 minutes or less.

[tex]=P(X\leq 4)\\=1-e^{-4/4} =0.6321[/tex]

(c) 5 minutes or less.

[tex]=P(X\leq 5)\\=1-e^{-5/4} =0.7135[/tex]

(d) longer than 5 minutes.

=1-P(X≤5) = 0.2865

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