Some Internet companies sell a service that will boost a web

Some Internet companies sell a service that will boost a website\'s traffic by delivering additional unique visitors. Assume that one such company claims it can deliver 800 visitors a day. If this amount of website traffic is experienced, then the time between visitors has a mean of 1.80 minutes (or 0.5556 per minute). Assume that a website gets 800 visitors a day and that the time between visitors has an exponential distribution.

a. What is the probability that the time between two visitors is less than 2 minutes ?
b. What is the probability that the time between two visitors is less than 3 minutes?
c. What is the probability that the time between two visitors is more than 4 minutes?

Solution

a)

The mean of the distirbution is also the standard deviation, and is equal to 1/lambda:          
          
mean = standard deviation = 1/lambda =    1.8      
          
The left tailed area in an exponential distribution is          
          
Area = 1 - e^(-lambda*x)          
          
As          
          
x = critical value =    2      
          
          
Then          
          
Area =    0.670807012   [ANSWER]

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b)

The left tailed area in an exponential distribution is          
          
Area = 1 - e^(-lambda*x)          
          
As          
          
x = critical value =    3      
          
          
Then          
          
Area =    0.811124397   [ANSWER]

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c)

The right tailed area in an exponential distribution is          
          
Area = e^(-lambda*x)          
          
As          
          
x = critical value =    4      
          
          
Then          
          
Area =    0.108368023   [ANSWER]