Reference no: EM131044408

Assignment 1

Task

QUESTION 1 Probability Show all calculations/reasoning

(a) Describe the classical method of determining probability. Give an example.

(b) What is the difference between a discrete probability distribution and a continuous probability distribution? Give your own example of each.

(c )Consider the following record of sales of lottery tickets for the last 50 days.

1. What was the probability of selling 9 or 10 units on any one day?
2. What were the average daily sales?
3. What was the probability of selling 10 or more?
4. What was the probability of selling 11 or less?

(d) A class contains 40 students. 12 are female (F) and Australian citizens (A); 14 are male (M) and Australian citizens) (A); 10 are female and overseas citizens (OS); 4 are male and overseas citizens (OS).

1. Using Excel construct a table showing gender in the rows and citizenship in the columns with total of rows and columns. Then paste this Excel table into Word.

2. Now calculate the probability of a student being:

(i) Male
(ii) Overseas student
(iii) Australian given a female
(iv) Overseas student given a male

(e) The time to complete a construction project is normally distributed with a mean of 50 weeks and a standard deviation 10 weeks.

1. What is the probability that the project will be completed in 54 weeks or less?
2. What is the probability that the project will be completed in 62 weeks or less?
3. What is the probability that the project will take longer than 70 weeks?

QUESTION 2 Research Question, Constructing data table and calculating probabilities

The following question involves learning/employing research skills in searching out data on the Internet, presenting it in a well constructed and informative table, and calculating some probabilities showing calculation methods.

1. Search the Internet for the latest figures you can find on the age and sex of the Australian population.

2. Then using Excel, prepare a table of population numbers (not percentages) by sex (in the columns) and age (in the rows). Break age into about 5 standard groups, eg, 0-14, 15-24, 25-54, 55-64, 65 and over. Insert total of each row and each column. Paste the table into Word as a picture.Give the table a title, and below the table quote the source of the figures.

3. Calculate from the table, showing your calculation methods:

The probability that any person selected at random from the population is a male.

The probability that any person selected at random from the population is aged between 25 and 54.

The joint probability that any person selected at random from the population is a female and aged between 15 and 24.

The conditional probability that any person selected at random from the population is 25 or over given that the person is a male.

QUESTION 3 Statistical Decision Making and Quality Control Show all calculations/reasoning

(a) A company wishes to set control limits for monitoring the direct labour time to produce an important product. Over the past the mean time has been 20 hours with a standard deviation of 9 hours and is believed to be normally distributed. The company proposes to collect random samples of 36 observations to monitor labour time.

1. If management wishes to establish x-bar control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL.

2. If management wishes to use smaller samples of 9 observations calculate the control limits covering the 95% confidence interval.

3. Management is considering three alternative procedures in order to maintain tighter control over labour time:

Sampling more frequently using 9 observations and setting confidence intervals of 80 Maintaining 95% confidence intervals and increasing sample size to 64 observations Setting 95% confidence intervals and using sample sizes of 100 observations.

Calculate the control limits for each of the 3 alternatives.

Which procedure will provide the narrowest control limits? What are they?

(b) Hypothesis testing

ABC Company has retained a private consulting firm to determine methods that will reduce its inventory costs. The consulting firm assumes that the mean time between placement and receipt of an order is 120 days.

To test this assumption the production manager of ABC randomly selected 100 orders and found that the mean time until delivery was 118.5 days. Past experience indicates that the standard deviation of the lead time (sigma x) is 12 days.

Using an alpha level of 0.05 and a 2-tail test, determine whether there is sufficient evidence that the mean time is not 120 days? Explain your conclusion.

Assessment item 2

Task

The following collaborative research project requires you work in groups, each consisting of approximately 5 students. Please confirm your group composition with your lecturer.

You and a group of investors are interested in setting up a chain of child care centres in a number of Local Government Areas in Australia. In order to do this successfully you need to ensure that the regions you choose will support your business over the next 10 years. Your minimum criteria are:

- enough adults who are likely to have children (24-35)
- these adults have the funds to pay for child care (how you identify that is up to you but you need to document this criteria)
- enough children of child care centre age (0-5).

These are the minimum criteria - you should identify some more that you can use in this business decision.

Your task is to prepare a report to be presented to your co-investors which identifies two (2) Local Government Areas in Australia which meet your criteria. Your report should demonstrate how these Local Government Areas meet the minimum criteria above and additional criteria which you have identified. You should also identify additional statistical information that is required before a final decision is made to start building the first child care centre.

Your report should be professionally presented and contain appropriate references. You can select whether your group will present in a written report or make a Power-point presentation to the class. Doing a presentation to the class is a great way to gain confidence and experience in talking to large audiences. Making presentations and working in teams are important professional skills and are required in Masters level courses.

Assessment item 3

Task

QUESTION 1 Decision Analysis

Show all calculations to support your answers. You may follow the methods shown in the mp4 on Decision Analysis for a way to do part (b) of this question if you wish.

(a) Explain the process of using marginal analysis to solve decision problems with a square matrix (ie actions = states) involving discrete probability distributions describing the states of nature. What steps are taken in the process, providing your own simple example.

What are the advantages and disadvantages of using marginal analysis to solve decision problems?

(b) James Patterson is considering investing money in three alternative investments over a one-year period. Below are the expected profits from each investment given assumptions about the state of the economy:

(i) If James is an optimist which investment should he choose?
(ii) If James is a pessimist which investment should he choose?
(iii) Following the criterion of regret which investment should he choose?
(iv) If James believes that there is a 70% chance of a good economy which investment should he choose?
(v) What is the expected value of perfect information about the state of the economy?

QUESTION 2 Value of information

Show all calculations to support your answers. You may follow the methods shown in the mp4 on Value of info for a way to answer this question if you wish.

A manufacturer is trying to choose between two production methods (a1 and a2) for a new product. He considers that the probability of demand for the new product being good (s1) is 0.4 and the probability that demand will be poor (s2) is 0.6.

In evaluating the two production methods the manufacturer has calculated the following table of conditional profits:

(a) Which production method should be used? Show calculations.

The manufacturer asks a marketing consult for an opinion as to whether demand will be good or poor. From previous experience when the consultant has indicated that demand will be good she has been right 80% of the time, and when she has indicated that demand will be poor she has been right 70% of the time.

(b) Revise the prior probabilities in light of the consultant's track record.
(c) What is the posterior probability of good demand given that the consultant has indicated demand will be good?
(d) What is the expected net gain or loss from engaging the consultant? Should the consultant be engaged? Why?

QUESTION 3 Simulation

This is a work integrated assessment item. The tasks are similar to what would be carried out in the workplace.

A factory has a toolshop in which one person serves toolmakers and is paid $75 per hour. Toolmakers employed by the factory must go to the toolshop for new tools, and are paid $100 per hour. Over a period of time it has been noted that the time between arrivals of toolmakers at the toolshop and the time to serve a toolmaker are as follow:

(a) Using Excel set up a simulation model to simulate about 2 hours (120 minutes) from time zero, and determine whether one attendant is sufficient or whether it is profitable to place a second attendant in the toolshop.

(b) Provide the costs over the 2 hours for the toolmakers' lost time and for the attendant's wages.

Show the data and the model in two printouts: (1) the results, and (2) the formulas. Both printouts must show row and column numbers and be copied from Excel into Word. See Spreadsheet Advice in Interact Resources for guidance.

(c) Your manager has suggested that a reorganisation of the toolshop could reduce the time taken to serve the toolmakers by 2 minutes, ranging from 3 to 7 minutes per toolmaker (but with the same relative frequencies as in parts (a) and (b)). Change the data for service times in your model (copy the model to make the changes, keeping the original model intact). Write a report to your manager explaining your conclusions, suggesting how much might be spent on the reorganisation and still be as well off.

QUESTION 4 Regression Analysis and Cost Estimation

Charles Hospital has recorded the following Administrative Costs and two possible cost drivers over the last year.

(a) Using the High-Low method of cost estimation and Patient Load as the cost driver, what would be the resulting cost equation for Administrative Costs?

(b) Using Excel, perform three regression analyses to regress Administrative Costs against Patient Load, then against number of Emergency Procedures, then against both of them simultaneously. Paste your results into Word. State the cost equation from each. Analyse and comment on the results of each regression as you perform it and determine the best one to use as a basis for future use.

(c) If the simple regression using Patient Load were adopted, what would be the predicted overhead in a month when there were 1,000 Patients and 10 Emergency Procedures?

QUESTION 5 CVP Analysis

A bicycle manufacturer makes two types of 21-speed bicycles, Road Bikes and Track Bikes. He has sales staff who sell the bikes on commission. The following data are available:

Fixed costs per annum are $65,000.

Required:
(a) Calculate the unit contribution margin for each product.
(b) This year the manufacturer will specialise in making only Road bikes. How many does he need to sell to break even?
(c) If Road bikes are still the only product what is the breakeven sales volume for the year in sales dollars?
(d) He now decides to manufacture both bikes this year in the ratio of 3 track bikes to 1 road bike.
(i) How many of each bike must be sold to earn a profit of $88,000 before tax for the year?
(ii) How many of each bike must be sold to earn a profit of $105,000 after tax (of 30c in the dollar) for the year?

Assessment item 4

This assessment task covers all learning outcomes in the subject and has been designed for you to demonstrate your mastery of the subject material and your ability to employ decisions support tools in management decision making.

Requirements

The examination consists of:

1. 30 multiple choice questions selected from the learning outcomes for the whole subject

2. 2 long answer questions covering the following learning outcomes:

to be able to apply CVP analysis and linear programming to product mix decisions
to be able to solve scheduling problems (with particular emphasis on project management networks)