Summarize the case scenario of the Regional Call Center’s Washington, D.C. facility. Develop bar charts showing the mean and median current account balance. Construct a scatter diagram showing current balance on the horizontal axis and past due amount on the vertical axis.

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Case Study: Transforming Data Into Information

Overview
You are a supervisor at Regional Call Center’s Washington, DC, facility. Regional provides contract call center services for a number of companies, including banks and major retail companies. You have been with the company for slightly more than seven years, having joined Regional right after graduating with a master’s degree in business administration from Strayer University. After the monthly staff meeting, you were handed a new assignment by the company CEO. The assignment came out of a discussion at the meeting in which one of Regional’s clients wanted a report describing the calls being handled for them by Regional. The CEO had asked you to describe the data in a file called Regional Call Center and produce a report that would both graphically and numerically analyze the data. The data are for a sample of 57 calls and for the following variables:

  • Account Number.
  • Past Due Amount.
  • Current Account Balance.
  • Nature of Call (Billing Question or Other).

Instructions
Summarize the case scenario of the Regional Call Center’s Washington, D.C. facility.
Develop bar charts showing the mean and median current account balance.
Construct a scatter diagram showing current balance on the horizontal axis and past due amount on the vertical axis.
Compute the key descriptive statistics for current and past due amount.
Repeat task 4 but compute the statistics for the past due balances.
Compute the coefficient of variation for current account balances.
Write a 4–5-page report (including a cover page and a source list page) to National’s client that contains the results of the completed tasks along with a discussion of the statistics and graphs.

Calculate a mean or margin of error or a confidence level, provide an example from your current professional or personal life that describes a measurement that is normal and how much wiggle room on either side would be appropriate. When would you want a 95% confidence interval and when would you be interested in a 99% confidence level?

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Topic 1:

Results from surveys or opinion polls often report a range of values—the sample statistic plus or minus a margin of error (the resulting range is called a confidence interval). This tells us that the range is likely to contain the population parameter. How much wiggle room we provide is based on how much confidence we wish to have that the range contains the actual population mean. That confidence level is directly related to the middle “truth” area we will accept versus the dubious tail area we will reject–also known as alpha (α). The more confidence we wish to have—the more middle ground we will need to accept (more wiggle room) thus a smaller tail area. If we insist on a larger alpha (more dubious tail area) we narrow the middle ground we will accept and thus provide less wiggle room—so the more likely it is that we will miss the true average (and thus we have a lower confidence level). A 95% confidence level leaves 5% alpha. A 99% confidence level leaves 1% alpha.

Now, without calculating a mean or margin of error or a confidence level, provide an example from your current (or your future) professional or personal life that describes a measurement that is normal—and how much wiggle room on either side would be appropriate. When would you want a 95% confidence interval and when would you be interested in a 99% confidence level (a little more wiggle room—so a wider range)?

Topic 2

Two or more samples are often compared when we suspect that there are differences between the groups—for example, are cancer rates higher in one town than another, or are test scores higher in one class than another? In nursing, when might you want to know the mean differences between two or more groups? Describe the situation (what groups, what measurements) including how and why it would be used.

Explain the difference between mean and median. Is mean always larger than median? Explain the difference between µ and x . How do you determine which is appropriate to use in a problemExplain the difference between σ and s. How do you determine which is appropriate to use in a problem? What is the relationship between variance and standard deviation?

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For each Chapter, answer each question in your own words using no more than 2-3 properly constructed sentences (correct grammar, punctuation, spelling, etc.). Be sure to include support for any “choice” answers. Use declarative sentences, citing factual information based on definitions, procedures, etc.

Chapter 1

1. Explain the difference between a population and a sample (from a statistical point of view). (4pts)
2. Explain the difference between quantitative variable and qualitative variable. (4pts)
3. Explain the difference between descriptive statistics and inferential statistics. (4pts)

Chapter 2

1. For a dataset, without constructing of the frequency distribution table; how to obtain the class width of frequency distribution table if the number of classes is given? (2pts)

Note: Use the formula in the slides; here frequency distribution table is not provided.

2. Explain the difference between a frequency distribution table and a relative frequency distribution table (4pts)

Chapter 3

1. Explain the difference between mean and median. Is mean always larger than median? (4pts)

2. Explain the difference between µ and x . How do you determine which is appropriate to use in a problem? (4pts)

3. Explain the difference between σ and s. How do you determine which is appropriate to use in a problem? (4pts)

4. What is the relationship between variance and standard deviation? (2pts) 2

5. Explain the difference between range and interquartile range. (4pts)

6. Explain what the coefficient of variation is. What is the advantage of using it compared to standard deviation? (4pts)

Chapter4
1. Explain the meaning of “Event with equally likely outcomes”. (4pts)
2. Explain the difference between joint(nonexclusive) events and disjoint(mutually exclusive) events. (4pts)
3. Explain the difference between P(A) and P(A|B). What does it mean if they are equal in value? What does it mean if they are unequal in value? (4pts)
4. Explain the difference between P(A|B) and P(B|A). Must they be equal in value? (4pts)
5. Explain the difference between Permutation and Combination. (4pts)

Chapter 5
1. Explain what a discrete random variable is. List examples.(4pts)
2. What are the requirements for a discrete probability distribution? (4pts)
3. Explain what binomial probability distribution is. Hint: list requirements in slides.(4pts)

Chapter 6
1. Explain what a continuous random variable is. List examples. (4pts)
2. Explain some basic characteristics of Normal Distribution. (4pts)
3. What is the standard Normal Distribution? (2pts)
4. Explain the difference between a raw score (x value) and a standard score(z value). (4pts)
5. How to convert a raw score to a standard score; and how to convert a standard score to a raw score? (4pts) 3
6. Explain how to use Table 2 for each of the following intervals:

  • a) z < a (less than)
  • b) z > a (more than)
  • c) a < z < b (between)

Here a and b are constant z units. b is larger than a Describe the strategies we mentioned in class for theses 3 cases (6pts)

7. Explain what the Inverse Normal Distribution is. How would you figure out whether a problem is Normal Distribution type or Inverse Normal type? (4pts)

Suppose that the government decides to impose an excise tax of T on each unit of the commodity discussed in Exercise 1.3. What price will the consumers end up paying for each unit of the commodity?

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Exercises

Exercise 1.1 Ifx + y = 3 and x – 2y = -3, what are x and y ?

Exercise 1.2 Solve the following simultaneous equations.
2x + y = 9,
x – 3y = 1.

Exercise 1.3 Suppose the market for a commodity is governed by supply and demand sets defined as follows. The supply set S is the set of pairs (q,p) for which q – 6p = -12 and the demand set D is the set of pairs (q,p) for which q + 2p = 40. Sketch Sand D and determine the equilibrium set E = S n D, the supply and demand functions qS, qD, and the inverse supply and demand functions pS, pD.

Exercise 1.4 Suppose that the government decides to impose an excise tax of T on each unit of the commodity discussed in Exercise 1.3. What price will the consumers end up paying for each unit of the commodity?

Exercise 1.5 Find a formula for the amount of money the government obtains from taxing the commodity in the manner described in Exercise 1.4. Determine this quantity explicitly when T = 0.5.

Exercise 1.6 The supply and demand functions for a commodity are If an excise tax of T is imposed, what are the selling price and quantity sold, in equilibrium?

Think of some of the different structures we’ve added to the ‘structure-less set’ as we moved through the text. What type of structure have we imposed on sets? Also, what did you find most interesting about our chapter on The Axioms?

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Connection and history summary

Per the syllabus our last assignment of the course will deal with summarizing the connections among different fields of mathematics (via structure) as well historical points (The Axioms).

For this assignment,Think of some of the different structures we’ve added to the ‘structure-less set’ as we moved through the text. What type of structure (algebraic, topological, etc) have we imposed on sets? Also, what did you find most interesting about our chapter on The Axioms?

 

Demonstrate ability to create an Excel spreadsheet and preform statistical calculations in Excel. Differentiate what a question is asking and what statistical calculation to use in order to answer the question. Compute probabilities from a binomial distribution, a Poisson distribution, or a normal distribution. Use a binomial distribution, a Poisson distribution, or a normal distribution to solve problems.

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Module 4: Probability Distribution & Normal Distribution

Module Goals

After completing this module, students will be able to do the following:

  • Demonstrate ability to create an Excel spreadsheet and preform statistical calculations in Excel.
  • Differentiate what a question is asking and what statistical calculation to use in order to answer the question.
  • Compute probabilities from a binomial distribution, a Poisson distribution, or a normal distribution.
  • Use a binomial distribution, a Poisson distribution, or a normal distribution to solve problems.

Overview

Module 4 explores three different types of distributions: binomial distribution and Poisson distribution (Chapter 5), and normal distribution (Chapter 6). A Poisson distribution is based on an area of opportunity in which you are counting occurrences within an area such as time or space. Contrast this with the binomial distribution in which each value is classified as of interest or not of interest.  Finally, normal distribution is defined by its mean and standard deviation.

Demonstrate ability to create an Excel spreadsheet and preform statistical calculations in Excel. Differentiate what a question is asking and what statistical calculation to use in order to answer the question. Compute probabilities from a binomial distribution, a Poisson distribution, or a normal distribution. Use a binomial distribution, a Poisson distribution, or a normal distribution to solve problems.

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Module 4: Probability Distribution & Normal Distribution

Module Goals

After completing this module, students will be able to do the following:

  • Demonstrate ability to create an Excel spreadsheet and preform statistical calculations in Excel.
  • Differentiate what a question is asking and what statistical calculation to use in order to answer the question.
  • Compute probabilities from a binomial distribution, a Poisson distribution, or a normal distribution.
  • Use a binomial distribution, a Poisson distribution, or a normal distribution to solve problems.

Overview

Module 4 explores three different types of distributions: binomial distribution and Poisson distribution (Chapter 5), and normal distribution (Chapter 6). A Poisson distribution is based on an area of opportunity in which you are counting occurrences within an area such as time or space. Contrast this with the binomial distribution in which each value is classified as of interest or not of interest.  Finally, normal distribution is defined by its mean and standard deviation.

Investigate two different options in terms of size and/or shape for the deck and make a recommendation to your uncle on which is the preferred Create two different designs for the deck based on one or more simple 2D One can be a simple shape, the other design should be a composite shape. Construct a scale drawing of each and include in your report.

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Investigative report

Context

Brisbane house prices continue to boom as residents from interstate flock to Queensland to enjoy the warmer climate and accompanying lifestyle. Your uncle is thinking of cashing in on the recent surge in prices and is considering selling the family home to downsize to a smaller property, as his children have now grown up and left home. He has asked you to investigate the design and the installation of a deck, as he believes that this will add value to the property. The deck should be large enough to comfortably seat a family of six at an outdoor dining setting. The garden where the deck would be located is level.

During this unit, you have studied techniques for measuring and calculating area, volume, calculation of scale factors and drawing scale diagrams. You will be using these skills to create plans and diagrams that will form part of a design for the proposed deck for your uncle. These will be combined with calculations and mathematical justifications to form a written proposal to be presented to your uncle.

Task

Create a proposal outlining a plan for installation of a deck at your uncle’s home. Your proposal must include the following:

  • You will investigate two different options in terms of size and/or shape for the deck and make a recommendation to your uncle on which is the preferred
  • Create two different designs for the deck based on one or more simple 2D One can be a simple shape, the other design should be a composite shape. Construct a scale drawing of each and include in your report.

Present your findings as an investigative report which can be used by your uncle to understand the requirements of the design and installation of a deck. Importantly, you are to use an independent approach to address all stages of problem-solving and mathematical modelling, as outlined in the attached flow chart.

Demonstrate ability to create an Excel spreadsheet and preform statistical calculations in Excel. Differentiate what a question is asking and what statistical calculation to use in order to answer the question. Compute probabilities from a binomial distribution, a Poisson distribution, or a normal distribution. Use a binomial distribution, a Poisson distribution, or a normal distribution to solve problems.

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Module 4: Probability Distribution & Normal Distribution

Module Goals

After completing this module, students will be able to do the following:

  • Demonstrate ability to create an Excel spreadsheet and preform statistical calculations in Excel.
  • Differentiate what a question is asking and what statistical calculation to use in order to answer the question.
  • Compute probabilities from a binomial distribution, a Poisson distribution, or a normal distribution.
  • Use a binomial distribution, a Poisson distribution, or a normal distribution to solve problems.

Overview

Module 4 explores three different types of distributions: binomial distribution and Poisson distribution (Chapter 5), and normal distribution (Chapter 6). A Poisson distribution is based on an area of opportunity in which you are counting occurrences within an area such as time or space. Contrast this with the binomial distribution in which each value is classified as of interest or not of interest.  Finally, normal distribution is defined by its mean and standard deviation.