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gfields

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In summary, the probability that in a 10 minute period more calls will arrive than the system can handle is approximately 0.0165. This can be calculated by finding P\{X>5\} using the Poisson distribution with a mean of 2 calls every 10 minutes. This information can be used to determine the adequacy of the new system.

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gfields

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- #2

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What have you tried?

Obviously, we're going to work with a random variable X such that X is Poisson([itex]\lambda[/itex]) distributed. What do you think [itex]\lambda[/itex] is in this case?

- #3

gfields

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I understand that the mean before the old system was 2 calls for 10 minutes.

I need to define the segment unit to do the problem... 10 minutes??

The mean is already defined for me. 2

Defining the segment size would be next. I need some discussion here to understand exactly what to use.The event of interest would be P>5 correct?

Once this information is calculated...the Poisson table can be used to find the probability and a comment on the adequacy of the new system can be made.

- #4

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gfields said:I am taking this class online...no instructor...no interaction. I need some guidance on how to think this through. The book is helpful but still lacks clarity.

I understand that the mean before the old system was 2 calls for 10 minutes.

I need to define the segment unit to do the problem... 10 minutes??

Good!

The mean is already defined for me. 2

Also good.

Defining the segment size would be next. I need some discussion here to understand exactly what to use.The event of interest would be P>5 correct?

Indeed, you'll need to calculate [itex]P\{X>5\}[/itex]. You can use tables to calculate this, but you can also do it by hand easily:

[itex]P\{X>5\}=1-P\{X\leq 5\}=1-e^{-2}(1+2+\frac{2^2}{2!}+\frac{2^3}{3!}+\frac{2^4}{4!}+\frac{2^5}{5!})[/itex]

- #5

CellCoree

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Sure, I would be happy to help with your Poisson distribution problem. Let's break down the problem into smaller parts to make it easier to understand and solve.

First, we need to understand what a Poisson distribution is. It is a probability distribution that is used to model the number of events that occur in a specific time period, given the average rate of occurrence. In this case, the time period is 10 minutes and the average rate of occurrence is 2 calls every 10 minutes.

Next, we need to determine the probability that in a 10 minute period, more calls will arrive than the system can handle. To do this, we need to find the probability of having 6 or more calls in a 10 minute period, as 5 is the maximum number of calls the system can handle. This can be calculated using the Poisson distribution formula:

P(x ≥ 6) = 1 - P(x ≤ 5)

= 1 - e^(-2) (2^0/0! + 2^1/1! + 2^2/2! + 2^3/3! + 2^4/4! + 2^5/5!)

= 1 - 0.406

= 0.594

Therefore, the probability that in a 10 minute period, more calls will arrive than the system can handle is 0.594 or 59.4%.

I hope this helps you understand and solve the problem. Let me know if you have any further questions.

The Poisson distribution is a probability distribution that is used to model the number of occurrences of a certain event within a specific time or space interval. It is often used in situations where the events are independent and occur at a constant rate, such as the number of customers arriving at a store in a given hour.

The Poisson distribution is unique in that it only has one parameter, the mean or average number of occurrences, whereas other distributions may have multiple parameters. Additionally, the Poisson distribution is discrete, meaning that the possible outcomes are whole numbers, whereas other distributions may be continuous.

The formula for calculating the probability using the Poisson distribution is P(x) = (e^-λ * λ^x) / x!, where λ is the mean number of occurrences and x is the specific number of occurrences for which you want to calculate the probability.

The Poisson distribution can be applied in a variety of real-world scenarios, such as predicting the number of accidents on a highway in a given day, estimating the number of calls a call center will receive in a certain hour, or determining the number of defects in a manufacturing process.

Some key assumptions when using the Poisson distribution include that the events being modeled are independent of each other, the average or mean number of occurrences is constant, and the probability of an event occurring in a given interval is proportional to the length of the interval. It is also assumed that the events are rare, meaning that the probability of more than one event occurring in a given interval is very small.

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