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MBA604 Statistics Assignment 1 Part 1 1) (5 pts) An electronics company is about to launch a new product. If the serial number for each piece

An electronics company is about to launch a new product. If the serial number for each piece produced has the following format: LLNNN where L stands for any letter in the English alphabet and N is a number from 0 to 9, please answer the following:
a)What is the name of the counting rule used to find all the possible outcomes?
b)How many different items can be uniquely numbered?
2)
(5 pts)
A company needs to select an expert group of consultants to provide advice for a given project. How many possible selections consisting of 2 project managers, 2
legal advisors, 4 computer scientists and 3 systemsengineers can be selected if the company can pick from 4 project managers, 7 legal advisors, 5 computer scientists and 6 systems engineers? Think carefully about the counting rules involved before attempting to do any calculations.
3)
(5 pts)
Consider that you are a line manager in your current Corporation. There is a 0.50 probability that you will be promoted this year. There is a 0.65 probability that you will get a promotion or a raise. The probability of getting a promotion and a raise is 0.35. (Use letter P to denote promotion and letter R to denote raise.)
a. If you get a promotion, what is the probabilitythat you will also get a raise?
b. What is the probability that you will get a raise?
c. Are getting a raise and being promoted independent events? Explain using
probabilities.
d. Are these two events mutually exclusive? Explain using probabilities.
Please show all the steps in your calculations
Part 2
Two of the cylinders in an eight-cylinder car are defective and need to be replaced. If two
cylinders are selected at random, what is the probability that
a. both defective cylinders are selected?
b. no defective cylinder is selected?
c. at least one defective cylinder is selected?
You are requested to solve the problem using two different approaches:
1.(9 pts) Solve the problem using your knowledge from the theory of probability (chapter 4 in your e-text). If you wish to use letters in order to label the events: please let "D
1
" denote the event of the first cylinder selected, to be defective and let "D
2
" denote the event of the second cylinder selected, to be defective. If you find it helpful
you can construct a tree diagram for this problem.
2.(9 pts) Solve the problem using your knowledge on probability distributions (chp 5 &
6). It is important to justify your choice of probability distributionto use. You will need to decide whether your random variable is continuous or discrete and also need to identify whether the sampling carried out is with or without replacement. These steps will help you to identify the appropriate probability distribution to use.
3.(2 pts) Finally compare the two solutions. Elaborate on thecomputational complexity
of each one of them and the execution time when solving the problem by hand (allowing the use of a basic scientific calculator but not statistical software).

MBA604 Statistics Assignment 1 Part 1 1) (5 pts) An electronics company is about to launch a new product. If the serial number for each piece produced has the following format: LLNNN where L stands for any letter in the English alphabet and N is a number from 0 to 9, please answer the following: a) What is the name of the counting rule used to find all the possible outcomes? b) How many different items can be uniquely numbered? 2) (5 pts) A company needs to select an expert group of consultants to provide advice for a given project. How many possible selections consisting of 2 project managers, 2 legal advisors, 4 computer scientists and 3 systems engineers can be selected if the company can pick from 4 project managers, 7 legal advisors, 5 computer scientists and 6 systems engineers? Think carefully about the counting rules involved before attempting to do any calculations. 3) (5 pts) Consider that you are a line manager in your current Corporation. There is a 0.50 probability that you will be promoted this year. There is a 0.65 probability that you will get a promotion or a raise. The probability of getting a promotion and a raise is 0.35. (Use letter P to denote promotion and letter R to denote raise.) a. If you get a promotion, what is the probability that you will also get a raise? b. What is the probability that you will get a raise? Please show all the steps in your calculations
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Part 2 Two of the cylinders in an eight-cylinder car are defective and need to be replaced. If two cylinders are selected at random, what is the probability that a. both defective cylinders are selected? b. no defective cylinder is selected? c. at least one defective cylinder is selected? You are requested to solve the problem using two different approaches: 1. (9 pts) Solve the problem using your knowledge from the theory of probability (chapter 4 in your e-text). If you wish to use letters in order to label the events: Let "D 1 " denote the event of the first cylinder selected, to be defective. Let "D 2 " denote the event of the second cylinder selected to be defective, when the result (defective/non-defective) of drawing the first cylinder is unknown. Therefore, P(D 2 ) is the marginal/prior probability of the 2 nd cylinder selected and being defective, without knowing the selection result of the first cylinder. To reiterate, P(D 2 ) is a marginal/prior probability, not a conditional one. If you find it helpful you can construct a tree diagram for this problem. 2. (9 pts) Solve the problem using your knowledge on probability distributions (chp 5 & 6). It is important to justify your choice of probability distribution to use. You will need to decide whether your random variable is continuous or discrete and also need to identify whether the sampling carried out is with or without replacement. These steps will help you to identify the appropriate probability distribution to use. 3. (2 pts) Finally compare the two solutions. Elaborate on the computational complexity of each one of them and the execution time when solving the problem by hand (allowing the use of a basic scientific calculator but not statistical software). It is emphasised once more that in the first case you need to solve the problem without using any known probability distribution formulas. You only need to use your knowledge from chapter 4.
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MBA604 research proposal (30%) You are about to commence a new research project in a field of your choice. You are expected to write a report that constitutes a research proposal. You should carry out the following tasks and document them in your report: 1. Undertake a literature review highlighting the current state of the art. 2. Taking into account the current state of the art highlight the novelty and contribution to knowledge upon successful completion of your project. 3. Do a feasibility study to assess the likelihood of the project being completed and producing useful results. If possible, the feasibility study should contain some preliminary results (e.g. a pilot data set and initial data analysis). 4. Present the research methodology you plan to follow. Include a description of your planned approach for data analysis including the statistical techniques you are planning to use. 5. Produce a project plan for your research project (ideally to be presented with the aid of a Gantt chart) showing the breakdown of processes constituting the project, highlighting the dependencies between them and hence showing those that can be run in parallel. Decide and present the various deadlines, milestones and deliverables. If more than one person is to be involved specify which tasks will be delegated to whom. As part of your project plan comment on your contingency plan i.e. what alternative steps you have to follow in case your original planning fails. 6. Produce a costing report for the various resources you will need (manpower, equipment, consumables, consultancy, travel etc). 7. Highlight the relevance to beneficiaries, i.e. who will benefit by the business/research findings and how. 8. Briefly mention how the business/research findings will be disseminated (e.g. conferences, workshops, seminars, journal publications, press releases). 9. Present the track record of the investigators involved, demonstrating why they would be capable of undertaking and completing such a project. 10. Conclude and summarize your report.
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11. Include a reference and bibliographical list. Make sure you use a formal referencing scheme (e.g. Harvard, Vancouver). 12. If necessary include appendices to provide additional material relevant to the document. Minimum 1500 words, Maximum 2500 words (If you are exceeding the word limit, please move some material to the appendices)
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MBA604 Statistics Assignment 2 (35 pts) Problem 1 (12 pts, 2 pts per question) Consider a population of five items identical in appearance but weighing 9, 13, 15, 17, and 19 grams. 1. Determine the mean and the variance of the population . 2. How many possible samples can we have if we sample without replacement from the above population with a sample size of 2. Please justify your choice of counting rule to determine the number of possible samples. 3. Write down all the possible samples, either in a linear format (i.e. a simple list) or using a tree diagram. 4. Using the ten sample-mean values, estimate the mean of the population and the variance of x . 5. Compute the standard error of the mean. 6. What is the relevant theorem that describes the behaviour of the sample mean when repeated samples are taken? Briefly describe the theorem in your own words. Problem 2 Part A (7 pts) The bottling station in plant A of a fizzy drinks company fills cans with a nominal value of 330 ml. Five days before the annual maintenance of machinery, a sample of 16 cans is taken and the volume of liquid in each one measured. At the 5% level of significance test whether the bottling process is carried out accurately or whether the filling machinery needs calibration. Use both the critical and the p-value approaches. (You will find the data in table 1. Use only the first column of the table corresponding to plant A.) Part B (8 pts) The company owns another bottling station located in a different plant (plant B). The plant manager claims that the variance of the can volumes (in ml 2 ) of the 2 nd bottling process (plant B) is the same as that of the 1 st plant. A sample of 10 cans is taken from the bottling station in plant B and the sample standard deviation is found to be 4.001 ml. Using the value of the sample variance of plant A that you have already calculated, test the claim of the plant manager at the 5% level of significance, using the critical value approach. You do not need to use the data from table 1 that corresponds to plant B.
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Problem 3 (8 pts) Consider the sample data for plants A, B, C & D of the above company, which are tabulated in table 1. Test whether the four means are equal at the 5% level of significance. Perform a test that will compare all 4 means at once. We are not interested in pair-wise comparisons at this stage. Please show all the steps in your calculations. Table 1 plant A plant B plant C plant D 333 328 320 333 332 329 321 321 320 323 322 329 326 327 325 330 328 330 326 328 325 331 328 325 323 332 329 333 321 320 330 331 334 324 331 327 322 323 332 320 334 329 330 328 331 330 Guidelines Please read these guidelines very carefully. Use of the template file A template file “_MBA604_asn2.doc” has been provided. You are requested to write your answers in this template file without removing or altering the headings that have already been inserted. Please preserve the original fonts and formatting. You can insert as many extra lines as you need, depending on how much space your solutions will take. There is no need to include the assignment questions in the file that you will submit. The first two pages of the template file are used for marking. Please write your name and the submission date in the relevant boxes of the 1 st row of the table in page 1. After doing this, please start filling in your answers from page 3 onwards. File-naming convention The following file-naming convention must be used: _MBA604_asn2.doc Please do not rename the template file. The submission module on the VLE will automatically prepend your name when the file will be downloaded. Submit the document in “Microsoft Word 2003 format”, i.e. “.doc”. Unfortunately, other file formats (e.g. docx, pdf, zip or other compressed files) cannot be accepted. If
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Top Answer

Dear pkawesha, PFA for... View the full answer

Solutions_pkawesha_Probability.doc

Part 1
1) An electronics company is about to launch a new product. If the serial number
for each piece produced has the following format: LLNNN where L stands for any
letter in the English alphabet...

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