$Operations research$

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$Operations research$

See attached image for details. The use of statistical software such as maple is encouraged.

Statistics Math Software Probability

Pipe98

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Matchmaticians Operations research  File #1

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Answer 1

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The average number of arrival per hour is $\lambda=80/4=20$ students per 15 minute. We need to compute the probability that on a 15 minute interval, more than 25 students visit the website. We have
\[P(n)=\frac{\lambda^ne^{-\lambda}}{ n!}=\frac{(20)^ne^{-20}}{ n!}.\]
So
\[P[n>25]=1-\sum_{i=0}^{25}\frac{(320)^ie^{-320}}{ i!}=1-0.88782=0.11218=11.218\%.\]
So in $11.218\%$ of time, there will be more than 25 students on the website. I used the following website to compute the above sum:

https://stattrek.com/online-calculator/poisson.aspx

Erdos

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Erdos

0

The average number of arrival is 20 students every 15 minutes.
Erdos

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There is s typo in the second equation. The number 320 in both places should be replaced by 20.
Erdos

0

The final answer 11.218% is of course correct.
Pipe98

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Thanks for the answer you seem to understand this well. I have posted another question on an M/M/c queuing model, do you think you could answer that?

$Operations research$

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