Assessment item 1
Topics 1-2
Value: 10%
Due date: 13-Aug-2015
Return date: 03-Sep-2015
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Alternative submission method
Task
QUESTION 1 Probability
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(a) What is the meaning of mutually exclusive events? Give an example of two events that are (i) mutually exclusive, and (ii) not mutually exclusive.
(b) Explain the calculation of conditional probabilities for statistically independent events. Provide an example.
(c) Consider the following record of sales for a product for the last 100 days.
SALES UNITS NUMBER OF DAYS
0 5
1 25
2 35
3 25
4 10
100
1. What was the probability of selling 1 or 2 units on any one day?
2. What were the average daily sales units?
3. What was the probability of selling 2 units or more?
4. What was the probability of selling 3 units or less?
(d) An urn contains 20 marbles. 8 are red, 6 are green and 6 are blue. Marbles are drawn and then replaced after each draw.
Calculate the probability of drawing:
(i) a red marble on the first draw
(ii) a blue marble on the first draw and a red on the second draw
(iii) two green marbles in two draws
(iv) a blue marble on the second draw given a red on the first draw
(e) The time to complete a construction project is normally distributed with a mean of 70 weeks and a standard deviation 8 weeks.
(i) What is the probability that the project will be completed in 74 weeks or less?
(ii) What is the probability that the project will be completed in 92 weeks or less?
(iii) What is the probability that the project will take longer than 90 weeks?
(f)
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.
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 15 and 54.
? The probability that any person selected at random from the population is a male and aged between 15 and 24.
? The probability that any person selected at random from the population is 55 or over given that the person is a female.

QUESTION 2 Statistical Decision Making and Quality Control
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(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 minutes with a standard deviation of 9 minutes and is believed to be normally distributed. The company proposes to collect random samples of 81 observations to monitor labour time.
1. If management wishes to establish x ¯ control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL.
2. If management wishes to use smaller samples of just 9 observations calculate the control limits covering the 95% confidence interval. (Round final calculations to 2 decimal places).
(b)
Hypothesis testing
From prior experimentation a Consumer Group has found that the mean life of a certain brand of 60 watt light bulbs is 72 days of continuous usage and the standard deviation is 12 days.
The light bulb company has recently marketed their bulb as “new and improved, yielding longer life”. The Consumer Group purchased 36 bulbs and tested them. The average life of the bulbs tested was 75.2 days.
Does the mean of 75.2 present sufficient evidence to support the claim that the new bulbs have a longer life? Use hypothesis testing with an a level of 0.05 to justify your conclusion.
(Hint: Ho would read µ = 72, H1: µ 72 a one-tail test)

Rationale
This assessment task covers topics 1 and 2: Probability concepts and distributions, and Statistical decision making and quality control. It has been designed to ensure that you are engaging with the subject content. More specifically, it seeks to assess your ability to:
•apply probability concepts to decision making
•demonstrate problem solving skills in assessing, organising, summarising and interpreting relevant information for decision making
•demonstrate understanding of the application of statistical hypothesis testing to decisions, with particular emphasis on quality control
Marking criteria
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 decisions problems.
Laws of probability well understood and mostly applied without error to decisions problems.
Laws of probability understood and applied appropriately to decisions problems.
Laws of probability mostly understood and mostly applied appropriately to decisions 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 for 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
The assignment should be word processed with any Excel files pasted into Word with row and column numbers.
Your name and student number should appear on every page as a header or footer.
All calculations must be shown.
All references used should appear at the end in full.

Requirements
Assignments must be submitted through turnitin. Your lecturer will announce if a hard copy submission is required addition to turnitin submission.