QUESTION 1 Probability

Show all calculations/reasoning

Guide to marks: 18 marks - 4 for (a), 5 for (b), 6 for (c), 3 for (d)

(a) Define what is meant by a probability distribution.

What is the difference between a discrete probability distribution and a continuous probability distribution?

Give an example of your own for each type of distribution.

(b) Consider the following record of daily sales of a baker’s top selling loaf of bread over the last 100 days:

NUMBER SOLD NUMBER OF DAYS

0 5

1 15

2 20

3 25

4 20

5 15

Total 100

1. What was the probability of selling 3 or 4 loaves on any one day?

2. What were the average daily sales over the period?

3. What was the probability of selling 2 or more loaves on any one day?

4. What was the probability of selling 4 loaves or less on any one day?

(c) A coin is tossed twice. Calculate the probability of each of the following:

1. A head on the first toss.

2. A tail on the second toss given a head on the first toss

3. Two tails

4. A tail on the first toss and a head on the second toss

5. A tail on the first and a head on the second or a head on the first and a tail on the second

6. At least one head on the first two tosses

(d) The average sales of apples is 5000 with a standard deviation of 600.

1. What is the probability that sales will be greater than 5600 apples?

2. What is the probability that sales will be less than 5240 apples?

3. What is the probability that sales will be less than 4400 apples?

QUESTION 2 Research Question: Constructing data table and calculating probabilities

Guide to marks: 14 - 5 for 1, 5 for 2, 4 for 3

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 55 and 64.

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

• The probability that any person selected at random from the population is 55 or over.

QUESTION 3 Statistical Decision Making and Quality Control

Show all calculations/reasoning

Guide to marks: 18 marks - 4 for a(1), 4 for a(2), 2 for b(1), 3 for b(2), 2 for b(3), 3 for b(4)

(a) A company wishes to set control limits for monitoring the direct labour time to produce an important product. In the past the mean time has been 20 hours with a standard deviation of 5 hours and is believed to be normally distributed. The company proposes to collect random samples of 64 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 16 observations calculate the control limits covering the 95% confidence interval.

(b)

Hypothesis testing

Argon Advertising Agency has suggested to Specialty Store that it use mail circulars for the area within a 15 km radius of its store as its major source of advertising. Asked, “Why not extend the area beyond 15 km?” Argon’s representative answered: “Your average customer lives no more than 9 km from the store, so that 15 km will cover almost all your potential customers.”

The owner of Specialty Store was not convinced of the truth of this answer and decided to test the statement that the average customer lives no more than 9 km from the store. A sample of 50 customers was taken, and a mean travelling distance of 10.22 km was found.

Based on the sample results, test the hypothesis that the average customer lives no more than 9 km from the store at a significance level of = 0.05. Experience shows that = 5 km. Your answer should respond to the following four requirements:

1. Show the null and alternative hypotheses.

2. Calculate the critical value.

3. Sketch the situation.

4. Assess the appropriate conclusion.

END OF ASIGNMENT 1

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 problems 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 emphais 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 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 meaningfully 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

You should refer to the marking criteria for each assessment item. You should also follow the directions given in each question.

Requirements:

1. Present answers in the same sequence as the questions set.

2. 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

The following link provides study resources such as referencing, writing, grammar, punctuation and study planning:

http://student.csu.edu.au/study/resources

Requirements

This assignment must be submitted through Turnitin.

It is recommended that your name, student ID and page number are included in the header or footer of every page of the assignment.

Further details about submission in Turnitin are provided in On-line submission.

Show all calculations/reasoning

Guide to marks: 18 marks - 4 for (a), 5 for (b), 6 for (c), 3 for (d)

(a) Define what is meant by a probability distribution.

What is the difference between a discrete probability distribution and a continuous probability distribution?

Give an example of your own for each type of distribution.

(b) Consider the following record of daily sales of a baker’s top selling loaf of bread over the last 100 days:

NUMBER SOLD NUMBER OF DAYS

0 5

1 15

2 20

3 25

4 20

5 15

Total 100

1. What was the probability of selling 3 or 4 loaves on any one day?

2. What were the average daily sales over the period?

3. What was the probability of selling 2 or more loaves on any one day?

4. What was the probability of selling 4 loaves or less on any one day?

(c) A coin is tossed twice. Calculate the probability of each of the following:

1. A head on the first toss.

2. A tail on the second toss given a head on the first toss

3. Two tails

4. A tail on the first toss and a head on the second toss

5. A tail on the first and a head on the second or a head on the first and a tail on the second

6. At least one head on the first two tosses

(d) The average sales of apples is 5000 with a standard deviation of 600.

1. What is the probability that sales will be greater than 5600 apples?

2. What is the probability that sales will be less than 5240 apples?

3. What is the probability that sales will be less than 4400 apples?

QUESTION 2 Research Question: Constructing data table and calculating probabilities

Guide to marks: 14 - 5 for 1, 5 for 2, 4 for 3

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 55 and 64.

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

• The probability that any person selected at random from the population is 55 or over.

QUESTION 3 Statistical Decision Making and Quality Control

Show all calculations/reasoning

Guide to marks: 18 marks - 4 for a(1), 4 for a(2), 2 for b(1), 3 for b(2), 2 for b(3), 3 for b(4)

(a) A company wishes to set control limits for monitoring the direct labour time to produce an important product. In the past the mean time has been 20 hours with a standard deviation of 5 hours and is believed to be normally distributed. The company proposes to collect random samples of 64 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 16 observations calculate the control limits covering the 95% confidence interval.

(b)

Hypothesis testing

Argon Advertising Agency has suggested to Specialty Store that it use mail circulars for the area within a 15 km radius of its store as its major source of advertising. Asked, “Why not extend the area beyond 15 km?” Argon’s representative answered: “Your average customer lives no more than 9 km from the store, so that 15 km will cover almost all your potential customers.”

The owner of Specialty Store was not convinced of the truth of this answer and decided to test the statement that the average customer lives no more than 9 km from the store. A sample of 50 customers was taken, and a mean travelling distance of 10.22 km was found.

Based on the sample results, test the hypothesis that the average customer lives no more than 9 km from the store at a significance level of = 0.05. Experience shows that = 5 km. Your answer should respond to the following four requirements:

1. Show the null and alternative hypotheses.

2. Calculate the critical value.

3. Sketch the situation.

4. Assess the appropriate conclusion.

END OF ASIGNMENT 1

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 problems 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 emphais 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 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 meaningfully 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

You should refer to the marking criteria for each assessment item. You should also follow the directions given in each question.

Requirements:

1. Present answers in the same sequence as the questions set.

2. 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

The following link provides study resources such as referencing, writing, grammar, punctuation and study planning:

http://student.csu.edu.au/study/resources

Requirements

This assignment must be submitted through Turnitin.

It is recommended that your name, student ID and page number are included in the header or footer of every page of the assignment.

Further details about submission in Turnitin are provided in On-line submission.

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