Internal Code: MAS546
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.
(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).
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. Now calculate the probability of a student being:
(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:
Question 3 Statistical Decision Making and Quality Control:
(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:
A. Sampling more frequently using 9 observations and setting confidence intervals of 80
B. Maintaining 95% confidence intervals and increasing sample size to 64 observations
C. 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?
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.
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:
1. enough adults who are likely to have children (24-35)
2. 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)
3. 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.
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