Instatistics, the probability distribution is a broad field thatentails various branches. Among them is the Poisson, binomial,uniform, and normal distribution. These methods can be applied in thework environment as well. It is important to describe them and statehow they are used in a workplace.

1.Describe and give example on how Poisson Distribution is used in awork environment.

Theprobability distributions that are as a result of Poisson experimentsare referred to as the Poisson test. The outcomes can easily beclassified as either a failure or success. At the same time, thetotal number of successes that takes place in a given area iscertain. There is a relationship between the probability of successand the size of the region in which it takes place. Suppose there aresmall parts in any location, the chances of success in them arevirtually zero (Bremaud, 2017). There is no particular form that thespecified region should take and therefore can take any. The numberof events taking place within a given interval is provided by a modelof Poisson distribution. This can be applied in the work environmentof any organization. For instance, a firm may determine that it getsclients at an average of 2.5 during a noon hour. If it is estimatedthat the staffs available can handle to 5 visitors during that hour,the probability of receiving six clients can be computed meaning thatone important call will be unattended to. Poisson tables are verycrucial in working out such a problem. The situation can beacceptable to this particular firm depending on how cranky itscustomers are.

2.Describe and give example on how Binomial Distribution is used in awork environment.

Ina binomial distribution, there are only two possible outcomes thatcan result from an event. For any activity to be considered abinomial distribution, it must satisfy certain conditions. The numberof observations must be fixed. That is, the probability of the trialcan be figured out. Similarly, each observation occurs independentlyof one another. The chance of one event occurring or not occurringdoes not affect the other one in any manner. Lastly, the chances ofthe success or failure are the same in all the trials (Bremaud,2017). In any challenge where binomial distribution is applicable,the formula must be applied. For example, suppose the management ofcompany X has only five staff members. It is possible to find theprobability that three of the staff is males. It is evident that thepossible outcome is either a male or female. If trials are made inthis scenario, they will total to five. Suppose out of the fivetrials three of them are males, then that is a success. However, whenthe probability of success and failure are added, their total isequal to 1. This method can be used only in areas where there are twopossible outcomes and not more than that.

3.Describe and give example on how uniform distribution is used in awork environment.

Theuniform distribution falls under the category of continuousprobability. The continuous random process has to be defined by twointervals, a and b. The likelihood of the subinterval of a and b isequal to its length. The process is therefore said to be uniformlydistributed between these two intervals. The continuous uniformdistribution is different from the cumulative one. When the maximumlikelihood method is applied in the uniform distribution, thesmallest and largest sample estimator values are given by α and βrespectively (Bremaud, 2017). This kind of distribution can beimplemented to any company more specifically those that deal with thesales of any product. For instance, in a company that sells shampoo,if it estimates that the products sold in a day at minimum are 2,000and 5,000 at maximum, and provided that the uniform distribution isbetween these two figures, then the probability of any change can becalculated. For example, if it is expected that the value mightchange to 2,500 products and 3,000, the probability can be computed.This is because P (2500< X≤300) which will give [1/(5000-2000)][3000-2500]. The chances of the modification projected as a possibleoutcome can be known with certainty by the responsible department.

4.Describe and give example on how normal distribution is used in awork environment.

Normaldistributions are paramount and widely used as far as statistics isconcerned. It is used in cases where the random variables have realvalues, but their distributions are unknown. The central limittheorem is applicable in the normal distribution because when therandom variables are drawn, they usually converge to normal. That is,there is normal distribution provided the random variables are large.All the physical quantities must have normal distributions at least.Other results necessary can be drawn from the normal distributiontable once it is drawn. Just like other distributions, this one canalso apply to different companies. For instance, a company producingnuts and bolts may want to know the exact height of each of them asthey are produced from the machines. The first thing is to write aprobability density function as f(x) = [1/ (√2πδ)]е^{-(x-µ)2}/2δ^{2}.The value of е is usually provided, and µ is the mean whereas δ isthe standard deviation. It is important from this point that thedimension of a given interval is found out by transforming theprobability density function to a standard normal distribution. Theresults can then be read from a standard normal distribution table.

Conclusion

Thevarious types of distribution can be applied in the workingenvironment. The application may differ from one firm to the otherdepending on the activities carried out. It is important that aproper method is applied after analyzing the situation.

Reference

Brémaud,P. (2017). *DiscreteProbability Models and Methods: Probability on Graphs and Trees,Markov Chains and Random Fields, Entropy and Coding*.Cham, Switzerland : Springer.