Question

Activity 4

Answer the following questions. You are allowed to use online calculators such as Stat Trek Binomial, Poisson, ect calculators, just make sure to note the values you entered in your answer. A similar question has previously been answered but it's incorrect which is why I am reposting my own version of the question.

I would prefer if the calculator was used where applicable but show any work to solve the problem as well.

Suppose you are designing a computer server for students to log into to work remotely. You know that on average you will see ten students logging into the server per hour.

a) What is the chance that more than 15 students will log into the server in a particular hour?

b) What is the chance of seeing exactly 10 students log into the server in a particular hour?

c) What is the chance of fewer than 15 students logging into the server in a two-hour period?

d) In designing the server, you must decide the maximum number of students that it can accommodate at one time. The more students you allow it to accommodate, the more expensive it will be. But if more students attempt to log in during a single hour than it can accommodate, it will crash. How many students should you design it to accommodate if you want there to be at most a 1% chance that it will crash during any particular hour?

Answer 1

Given mean, students logging into the server per hour.

I am going to useStat Trek poisson calculator to solve this problem.

a) Here we want .

So, in the calculator, enter:

Poisson random variable (x): 15

Average rate of success: 10

and hit calculate. From output:

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b) Here we want .

So, in the calculator, enter:

Poisson random variable (x): 10

Average rate of success: 10

and hit calculate. From output:

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c) The average student in two hours would be

Here we want .

So, in the calculator, enter:

Poisson random variable (x): 15

Average rate of success: 20

and hit calculate. From output:

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d) Here they want maximum number of students that it can accommodate at one time if you want there to be at most a 1% chance that it will crash during any particular hour.

In symbolic form, we want to find value of k, such that .

Here, in the calculator, enter:

Average rate of success: 10

and change Poisson random variable (x): and see cumulative probability P(X>x).

At Poisson random variable (x): 17, P(X>17) = 0.01428 (which is greater than 0.01) and at Poisson random variable (x): 18, P(X>18) = 0.00719 (which is less than 0.01).

Since at Poisson random variable (x): 18, P(X>18) = 0.00719 is less than 0.01, the correct value of k should be .