Conditions for Using a Binomial Distribution

Conditions for Using a Binomial Distribution Binomial probability distributions are useful in a number of settings. It is important to know when this type of distribution should be used. We will examine all of the conditions that are necessary in order to use a binomial distribution. The basic features that we must have are for a total of n independent trials are conducted and we want to find out the probability of r successes, where each success has probability p of occurring. There are several things stated and implied in this brief description. The definition boils down to these four conditions: Fixed number of trialsIndependent trialsTwo different classificationsThe probability of success stays the same for all trials All of these must be present in the process under investigation in order to use the binomial probability formula or tables. A brief description of each of these follows. Fixed Trials The process being investigated must have a clearly defined number of trials that do not vary. We cannot alter this number midway through our analysis. Each trial must be performed the same way as all of the others, although the outcomes may vary. The number of trials is indicated by an n in the formula. An example of having fixed trials for a process would involve studying the outcomes from rolling a die ten times.  Here each roll of the die is a trial. The total number of times that each trial is conducted is defined from the outset. Independent Trials Each of the trials has to be independent. Each trial should have absolutely no effect on any of the others. The classical examples of rolling two dice or flipping several coins illustrate independent events. Since the events are independent we are able to use the multiplication rule to multiply the probabilities together. In practice, especially due to some sampling techniques, there can be times when trials are not technically independent. A binomial distribution can sometimes be used in these situations as long as the population is larger relative to the sample. Two Classifications Each of the trials is grouped into two classifications: successes and failures. Although we typically think of success as a positive thing, we should not read too much into this term. We are indicating that the trial is a success in that it lines up with what we have determined to call a success. As an extreme case to illustrate this, suppose we are testing the failure rate of light bulbs. If we want to know how many in a batch will not work, we could define success for our trial to be when we have a light bulb that fails to work. A failure of the trial is when the light bulb works. This may sound a bit backward, but there may be some good reasons for defining the successes and failures of our trial as we have done. It may be preferable, for marking purposes,  to stress that there is a low probability of a light bulb not working rather than a high probability of a light bulb working. Same Probabilities The probabilities of successful trials must remain the same throughout the process we are studying. Flipping coins is one example of this. No matter how many coins are tossed, the probability of flipping a head is 1/2 each time. This is another place where theory and practice are slightly different. Sampling without replacement can cause the probabilities from each trial to fluctuate slightly from each other. Suppose there are 20 beagles out of 1000 dogs. The probability of choosing a beagle at random is 20/1000 0.020. Now choose again from the remaining dogs. There are 19 beagles out of 999 dogs. The probability of selecting another beagle is 19/999 0.019. The value 0.2 is an appropriate estimate for both of these trials. As long as the population is large enough, this sort of estimation does not pose a problem with using the binomial distribution.

Case write up- Marketing Essay Example | Topics and Well Written Essays - 500 words

Case write up- Marketing - Essay Example Lack of professional management therefore has resulted into the lack of organizational development which could have been translated into greater success for the firm at the international level. 3. Another important key issue is the lack of capital to expand the business not only in the local market but at the international level too. Lack of capital has forced the firm to actually limit it and grow organically rather than expanding itself into new and emerging market. This has indirectly resulted into lack of exposure for the firm at the international level besides restricting its growth capacity. 1. Market expansion should be considered as one of the important strategic moves by the firm to actually ensure that it expands into the market other than Europe. Market expansion can be achieved either through the formation of strategic alliances with the firms which are already operating in the target markets of the firm or through a direct entry into the market. 2. Product development can be another important strategic move which the firm can make in order to ensure that they offer a variety of products to the existing market. As described in the case that the retailers often take very few items during the season and the firm is still not in men’s or children business therefore to offer a variety to the market, it is critical that new products should be rolled out at relatively quicker pace in the existing market. In order to ensure that the firm becomes successful at the international level, it is important that the strategy of market expansion must be adapted. In order to expand, business needs to formulate strategic alliances with the firms working in other markets. The formation of strategic alliances can really offer the firm a real chance to know and understand the market with relatively lesser capital while at the same time gaining valuable entry into a new market. Strategic alliances could be formed either through the

Strain Theory Thesis Example | Topics and Well Written Essays - 3500 words

Strain Theory - Thesis Example It is therefore critical that criminology as a social issue is given multidimensional approach that will consider various observed behaviors. The social environment is significant in influencing the behavior and conduct of individuals and this explain crime rate differences across gender. While studying the crime theory, it would be important to highlight such social parameters that influence behavior outcomes in people. In this case strain theory would serve as an important theory to unveil the causes of crime in the society. In various disciplines there are theories that explain a given phenomenon and criminology is not exceptional. Many scholars and researchers have diverse definition of theory but the common denominator is the aggregate application in explain any observed phenomenon in the society. Theory is generally a set of principles that are devised to explain a group of facts. It emphasizes proof of ideas behind principles that have repeatedly been tested and widely accepted as responsible for a given phenomenon. In regard to strain theory, it explains the factors that push an individual to develop criminal behavior in the society (Agnew, 2006). Although each man is born free, the emerging character is shaped by many external environment factors and this serves even crime mind development. Criminological theory plays a central role as far as understanding of crime is concerned. Past research indicates that criminology theory explains the forces behind emotional and psychological transformation t hat shapes a criminal mind. There are incidences across the world where people commit outrageous crimes that one can never imagine of. The mitigation measures towards reoccurrence of such criminal acts require understanding of theory of criminology. Development of theory constitutes critical analysis of a given phenomenon by establishing the variables and their relationship. Such relationship among variables must be taken through a

Animal Symmetry Essay Example for Free

Animal Symmetry Essay 1. Animals with radial symmetry function differently than animals with bilateral symmetry. Unlike animals with bilateral symmetry, these organisms use their appendages, usually tentacles, to bring in food to its mouth, which is located at its center. Also, animals with radial symmetry have less complicated systems than animals with bilateral symmetry. The radial symmetry body plan involves appendages radiating out from the center of the organism, this means that most systems are not included in these animals. Since the radial symmetry body plan has little to no systems, this makes the animals less intelligent than the bilateral symmetry body plan. This means animals with radial symmetry cannot react as well as other animals. This also means the organism cannot, see, taste, smell, or think as well, as bilateral symmetry animals. Due to this disability, any animal that follows this body plan has adapted to be able to react without these senses. Though this makes it harder for the animal to function, by using a different life style it can survive. The cnidarian eats by pulling food in with its tentacles. This lack of senses means that the cnidarian relies on prey swimming into its tentacles. After eating, the waste then exists the way it entered, through the mouth. These animals have limited motion, relying mainly on currents to move, or not even moving at all. Cnidarians also reproduce fairly simply. When they reproduce asexually, they bud. This means that a new cnidarian grows off of an existing one. When they reproduce sexually, the female makes an abundance of eggs, and the male secretes sperm in the hope of fertilizing the eggs. That is the lifestyle of the cnidarian.

Animal Testing Needs To Stop Essay -- essays research papers

Cosmetic and drug companies should stop animal testing. By animal testing, the companies not only violate the animals' rights (which is breaking the law), but their testing methods are hazardous which endanger the animal's life. Finally, the companies should stop animal testing because each year we lose hundreds of thousands of animals and could make a difference by stopping this cruelty. Stop the animal testing, and save a life. To start with, cosmetic and drug companies should stop animal testing their products. By animal testing, they not only violate the animals' rights- they are breaking the law. Animals cannot speak for themselves so when they are unwillingly tested on, they cannot say anything in their own defense. The companies that test on animals violate the rights that were given to all living beings-including animals. As most know, this is illegal to break the law, yet still they get away with it. Who wants these companies taking charge of our rights- our freedom? Therefore, animals should not be used as lab specimens just so we humans can indulge ourselves in beauty products. Take a stand against animal testing, immediately, and stop this brutal treatment that is being done to these defenseless animals. Above all, help save their lives, and help show others how important it is that people know just how big of a difference they can make. In addition to breaking the law and violating animal rights, the cosmetic and drug companies endanger the helpless animals with their destructive testing methods and procedures. Scientists have tested up to twenty animals at a single time. In that experiment, each individual animal died. Their testing methods are not only horrible, but they are deadly. Whethe... ... To review, animal testing does nothing helpful to anyone except to cover up themselves with fashionable beauty products in which hundreds of thousands of innocent animals die every year. The companies that test violate the animal?s rights and at the same time, break the law. Animal testing for medicines, and make up is unreasonable and cruel to the animal. Finally, the companies testing methods are hazardous and deadly, and endanger the animal?s life- if they do not die first. Animal testing should be stopped and ban from ever being done again. Animal testing is not a requirement and therefore it does not have to be done. There are alternatives to animal testing and yet we fail to see them. By stopping animal testing, you can save hundreds of thousands of animals a year. These animals do not deserve to be treaty so viciously. Stop animals testing and save a life.

Convicting, Convincing, and Converting Essay

The argument most reliable is convicting, converting, and convincing. Many denominational Churches and spiritual beliefs have conflicting feelings around this issue. Many feel that they can take in their rules or pick and choice the Scriptures (cherry-cream) and translate to accommodate their demands. â€Å"The Bible is supernatural in focus† (Towns, 2007 p. 19). Now by doing such blasphemy activities, one is defying God’s authority. That sort of behavior only leads to wicked spirits. Most importantly, we should not pick and choose Bible verses to suit our situations. God has laid out all of His commands systematically, and no short cuts. I have come across this dilemma in several churches. You see, when I became born again, The Holy Spirit condemned me of my past and enable me to see God through His eyes. The Word convinced me. I empowered the Almighty to be my Redeemer; God worked in me. Today, The Almighty God has granted me the pass for everlasting life and supply me with a passport of Heaven. In conclusion, Elmer Towns states the Bible is an awesome comforter and provider. â€Å" Perhaps the greatest influence of the Bible is its convicting, convincing, converting power to all who honestly accept its message and believe in Jesus Christ† (Towns, 2007 p. 24). The Word provides the reading audience a powerful belief of God being the real and a big deal. He is not the Author of confusion. (1 Corinthians 14: 33) For God is not the author of confusion, but of peace, as in all churches of the saints (KJV). We must be aware that God comes to make peace with us. Once one has agreed to accept a spiritual relationship with God, you adopt off the former and bring on a new. Why not test Him and partake of the promise He has put aside for you to experience eternal life by keeping His commandments.

What is The Scientific Method, and How is The Theory...

What is the scientific method ,and how is the theory applied to fingerprint analysis? The complete friction ridge identification process involves using the identification philosophy and scientific methodology in determining whether or not an unknown friction ridge impression(herein, called latent) came from the same source as a known inked print (herein called print)to the exclusion of all others. (1) David Ashbaugh refers to this identification process as, a guide of how friction ridge quantative-qualititive analysis is transformed into an opinion of individuality. It describes the friction ridge formations used during analysis while establishing parameters as to how much knowledge one must have to perform such a task. Analysis,†¦show more content†¦Red Flags are abnormalities in the lift and provide many cautions. They are contained within the latent or surrounding areas . These include: *Double taps *Similar shaped ridge path formations *Matrix smears *Colur reversals *Inconsistancies in ridge width *Light or dark areas *Sudden directional change in ridge flow. *Does the lift appear consistant with the surface from which it was lifted? When a Latent Print Examiner considers any of these red flags, and howShow MoreRelatedForensic Science And Criminal And Civil Law Enforcement843 Words   |  4 Pagestaken decisive measures to minimize crime, and in doing so, turned to the scientific community for assistance, and technical support. As such, criminal investigation revolves around three particular questions: 1. who committed the crime? This question is answered based on witnesses, and evidence collection and comparison, 2. how was the crime committed? 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