The time in minutes for which a student uses a computer terminal at the computer

Question

The time in minutes for which a student uses a computer terminal at the computer center of a major university follows an exponential probability distribution with a mean of 37 minutes. Assume a student arrives at the terminal just as another student is beginning to work on the terminal.

What is the probability that the wait for the second student will be 15 minutes or less (to 4 decimals)?

What is the probability that the wait for the second student will be between 15 and 45 minutes (to 4 decimals)?

What is the probability that the second student will have to wait an hour or more (to 4 decimals)?

Explanation / Answer

Solution:

From the given information
Exponential probability distribution with a mean = 37 minutes

P(wait time 15 mins)
= 1 - e(-15 / 37)
= 0.3332

P(15 mins wait time 45 mins)
= (1 - e(-45 / 37)) - (1 - e(-15 / 37))
= 0.3704

P(wait time 60 mins)  
= 1 - (1 - e(- 60 / 37))
= 0.1976

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