Chapter 5 Statistice in Practice Citibank, the retail banking division of Citigr

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Chapter 5 Statistice in Practice

Citibank, the retail banking division of Citigroup, offers a wide range of financial services including checking and saving accounts, loans and mortgages, insurance, and investment services. It delivers these services through a unique system referred to as Citibanking.

Citibank was one of the first banks in the United States to introduce automatic teller machines (ATMs). Citibank’s ATMs, located in Citicard Banking Centers (CBCs), let customers do all of their banking in one place with the touch of a finger, 24 hours a day, 7 days a week. More than 150 different banking functions—from deposits to managing investments—can be performed with ease. Citibank customers use ATMs for 80% of their transactions.

Each Citibank CBC operates as a waiting line system with randomly arriving customers seeking service at one of the ATMs. If all ATMs are busy, the arriving customers wait in line. Periodic CBC capacity studies are used to analyze customer waiting times and to determine whether additional ATMs are needed.

Data collected by Citibank showed that the random customer arrivals followed a probability distribution known as the Poisson distribution. Using the Poisson distribution, Citibank can compute probabilities for the number of customers arriving at a CBC during any time period and make decisions concerning the number of ATMs needed. For example, let  arriving during a one-minute period. Assuming that a particular CBC has a mean arrival rate of two customers per minute, the following table shows the probabilities for the number of customers arriving during a one-minute period.

Each Citicard Banking Center operates as a waiting line system with randomly arriving customers seeking service at an ATM.

© Chris Pancewicz/Alamy.

x

Probability

0

.1353

1

.2707

2

.2707

3

.1804

4

.0902

5 or more

.0527

Discrete probability distributions, such as the one used by Citibank, are the topic of this chapter. In addition to the Poisson distribution, you will learn about the binomial and hypergeometric distributions and how they can be used to provide helpful probability information.

Read the "Statistics in Practice" article and answer the following questions: Think about Chapter 5 and its description of a Binomial random variable and a Poisson random variable. Provide an example of either one of these random variables that occurs in daily life. Obviously, do not use the example in the article, but think about another random variable that would satisfy the characteristics of either the Binomial or the Poisson. Feel free to use the Web to identify sources that support your examples and cite any sources you use. Be specific in your reply.

x

Probability

0

.1353

1

.2707

2

.2707

3

.1804

4

.0902

5 or more

.0527

Explanation / Answer

Binomial distribution is used to model such events which have outcomes that can have two states (one of the event happening and the other of the event not happening).The binomial distribution has assumption that n and p should be fixed throughout the experiment and all the trials should be independent of each other .To quote a few ,

1)  Xi : No. of students that passed the exam and it is said to have parameters n=20 and p=0.6 ,which can be interpreted as we would fit a model on 20 students whose probability to pass the exam is 60%.

2. Yi :No. of days it rained where n=20 gives number of days and p=0.5 states that there is 50% chance of raining everyday.

3. Zi : No. of matches won by a cricket team where n=10 gives the total matches played and p=0.4 is the probability of winning the match .

4. Ai : No. of patients cured by the end of the treatment ,having n=25 and p=0.8 ,is used to model the no. of patients who would either be cured or not cured by the end of the treatment

Poisson Distribution is used to model such events which are rare to occur and their probability of occurrence is low.

The assumptions pertaining to Poisson distribution is that each event must be independent of each other and the number success is modelled by mean no. of successes. Few of the real-life examples are :

1) No. of phone calls in a fire station per day can be modelled by Xi ~Poi(10) where 10 is the average number or rate of calls per day

2) Yi : No. of accidents on highway per month where Yi ~Poi (20) where 20 is the no. of average rate of accidents on highway

3) No. of students student in a class who participate in school fest every year with a mean rate of 3 per year .

4) No. of typos (typing error) in a page of a novel with mean of 5 typos per age.

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