Question

From “Just-In-Time” delivery and inventory control in a warehouse, to customer service at a call center, to line management at Disneyland, sometimes knowing how many customers you have is not as important to know how fast they are piling up. In this Project you will need to collect real world data, use it to build a model, and then use that model to assess a second set of data that you will also collect.

First you need to decide what you are going to measure. It needs to be something that can be counted during a time interval. Examples include but are not limited to: Customers queuing up at a SUBWAYtm ; Cars entering a parking lot; Students walking past your dorm room window. You will take this count for an interval of at least one hour. For the first data set, you should have a count of at least five. (So you will need to use Personal Probability to make an appropriate choice of measurement.) Use this first count to construct a Poisson Distribution that models the number of “Events” per hour.

Note: If you are observing a business you should be sure to have their permission to loiter as well as track their customers. Even observing a public space, such as a park or a dorm, should be done with care and respect. If you are measuring traffic patterns, be sure to take all appropriate safety precautions.

On a different day, make the same measurements, again for at least one hour. If this new count is less than the average value given by your model, what is the total probability that your model would produce that value or less? If it is greater than the average, what is the total probability your model would produce that value or greater? How does this new information effect your confidence in the original model? What additional factors might explain the similarities/differences between the two counts?

people coming into my work for an hour-

first day: 28

next day:32

Answer 1

By using Poisson distribution we construct the data for a people coming to work on the first day and at next day

P(X=x) = xe-  / x!

=np

For the first day, X=at least five which mean we have to calculate Poisson data till 28 and 60 which we take means per hour

P(X>28)= 1-P(X<27)= 0.874

For the next day, X=at least one

P(X>32)= 1-P(X<31)= 0.937

so by calculating the Poisson distribution, we can find out the data by putting these value