QUESTION 1 Probability Show all calculations/reasoning Guide to marks:

(a) 3, (b) 3, (c1) 5, (c 2-6) 5 (1 each), (d) 4 (1 each)

(a) Define the term probability. How is it measured? What range can the measures take and what do they mean?

(b) What is meant by the term statistical independence? How can it be identified from a relationship between two variables in a given situation?

(c ) Consider the following record of daily sales of loaves of sourdough bread over the last 100 days. . Sales Units (x) No. of days p(x) Exp value More than Les than [x-E(x)]2 [x-E(x)]2 p(x) 0 5 1 15 2 20 3 25 4 20 5 15 Total 100 Variance (1)Copy the above table into Excel and using formulas complete the missing column figures (note that the 5th and 6th columns refer to cumulative probability distributions) while the last 2 columns contain variance calculations.

All cells (except for cols 1 and 2) are to contain formulas so no fudging. Answer the questions below by highlighting the answers in your table, and simply repeating these figures against answers 2 to 6. After answering the questions below paste your Excel model into Word twice, once showing the output and once showing formulas (with row and column headings). Insert the standard deviation below the variance.

(2) What were the average daily sales? Highlight your answer in the spreadsheet and repeat it here.

(3) What was the probability of selling 2 or more loaves on any one day? Highlight your answer in the spreadsheet and repeat it here.

(4) What was the probability of selling 2 or less? Highlight your answer in the spreadsheet and repeat it here.

(5) What is the variance of the distribution? Highlight your answer in the spreadsheet and repeat it here.

(6) What is the standard deviation? Highlight your answer in the spreadsheet and repeat it here.

(d) The average sales of oranges is 4,700 with a standard deviation of 500.

(1) What is the probability that sales will be greater than 5,500 oranges?

(2) What is the probability that sales will be greater than 4,500 oranges?

(3)What is the probability that sales will be less than 4,900 oranges?

(4) What is the probability that sales will be less than 4,300 oranges?

QUESTION 2 Research Question, Constructing data table and calculating probabilities Guide to marks: - (1) 3, (2) 3, (3) 4 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. 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 female. .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 male and aged between 55 and 64. .The conditional probability that any person selected at random from the population is aged between 25 and 64 given that the person is a female.

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

3 each for 1,2, and 3, 1 for conclusion, (b) 10: 2 for 1, 3 for 2, 2 for 3, 3 for 4 (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 30 hours with a standard deviation of 10 hours and is believed to be normally distributed.

The company proposes to collect random samples of 64 observations to monitor labour time. If management wishes to establish x-bar control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL.

If management wishes to use smaller samples of 16 observations; calculate the control limits covering the 95% confidence interval. Management is considering three alternative procedures in order to maintain tighter control over labour time: Sampling more frequently using 16 observations and setting confidence intervals of 90% Maintaining 95% confidence intervals and increasing sample size to 64 observations Setting 95% confidence intervals and using sample sizes of 36 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 Active Insurance Company's rates for fire insurance depend on the distance a home is from the nearest fire station.

A progressive community claims that the average home in its town is within 5.5 km of the nearest fire station. Active took a sample of 64 homes, which produced a mean of 5.8 km from the nearest fire station. Is there sufficient evidence to refute the town's contention that the mean distance is not greater than the claimed 5.5 km if ? (sigma) = 2.4 km? Use ? = 0.05.

1. Show the null and alternative hypotheses.

2. Calculate the critical value.

3. Should the town's claim be accepted or rejected?

4. Sketch the situation.

Rationale back to top This assessment task will assess the following learning outcome/s: be able to demonstrate problem-solving skills in assessing, organising, summarising and interpreting relevant data for decision making purposes. be able to apply decision theory to business situations. be able to demonstrate understanding of the application of statistical hypothesis testing to decisions, with particular emphasis on quality control and interpreting the significance of regression coefficients in cost estimation. Marking criteria and standards back to top

Assessment Item 

The criteria described below will not apply to all parts of all questions but describe the standards expected where the question requirements are appropriate. It is expected that all students will complete their own work with no collusion with other students.

Criteria High distinction Distinction Credit Pass Apply probability concepts to decision making Laws of probability well understood and applied without error to decision problems Laws of probability well understood and mostly applied without error to decision problems Laws of probability understood and applied appropriately to decision problems Laws of probability mostly understood and mostly applied appropriately to decision problems Assess, organise, summarise and interpret data Search the internet for appropriate data and summarise into tables and interpret meaningfully Search the internet for appropriate data and summarise into tables and interpret Search the internet for appropriate data and summarise into tables that can be interpreted meaningfully Search the internet and find appropriate data and summarise into tables that can be interpreted

Apply statistical hypothesis testing to decisions with some emphasis on quality control Use of sample data to determine whether a statistical process is in control, with complete understanding of the relevant use of Z scores and t scores Use of sample data to determine whether a statistical process is in control, with mostly good understanding of the relevant use of Z scores and t scores Use of sample data to determine whether a statistical process is in control, with some understanding of the distinction between the use of Z scores and t scores Use of sample data to determine whether a statistical process is in control, with some understanding of the use of Z scores but less understanding of the use of t scores Presentation back to top You should refer to the marking criteria for each assessment item. You should also follow the directions given in each question.

Requirements: Present answers in the same sequence as the questions set. The front page of your assessment should consist of: subject code and subject name your name and student number assessment item number

3. Other pages should include: statement of academic integrity list of questions attempted student name and number on each page submitted pages should be numbered bibliography on last page.