Some Internet companies sell a service that will boost a website\'s traffic by d
ID: 3390471 • Letter: S
Question
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?
Explanation / Answer
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]
******************
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]
********************
c)
The right tailed area in an exponential distribution is
Area = e^(-lambda*x)
As
x = critical value = 4
Then
Area = 0.108368023 [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.