**QUESTION 1 Probability****Show all calculations/reasoning**

Student guide to marks: 29 - 4 for a, 6 for bl, 2 each for b2-b6, 6 fo c,3 for d

(a) What is the meaning of the term 'expected value', and what does it measure? How is it computed for a discrete probability distribution? Demonstrate your answer with a practical example.

(b) Consider the following record of daily sales of loaves of sourdough bread over the last 100 days.

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).

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 3 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.

(c) A lot of 10,000 parts, produced on four machines, was graded according to three grades. These results were:

(c) A lot of 10,000 parts, produced on four machines, was graded according to three grades. These results were:

What is the probability that a part selected at random:

1. Was produced by Machine W and should be reworked?

2. Was produced by Machine Z and is not satisfactory?

3. Was produced by Machine Y and should be scrapped?

4. Needs to be reworked?

5. Needs to be scrapped given that it was produced by machine W?

**(d) The average sales of apples is 4000 with a standard deviation of 500.**

1. What is the probability that sales will be greater than 4250 apples?

2. What is the probability that sales will be less than 3600 apples?

3. What is the probability that sales will be less than 4500 apples?**QUESTION 2 Research Question**

The following question involves learning/employing research skills in searching out data on the Internet

Search the Internet for the latest figures you can find to answer the following questions:

1 What is the average age of the Australian population?

2 What is the average age to die in Australia (for both men and women)?

3 What percentage of people work in Australia?**QUESTION 3 Statistical Decision Making and Quality Control**

Show all calculations/reasoning**Student guide to marks: 15 - 3 for al, 4 for a2, 8 for b (2 each)**

(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 6 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 9 observations calculate the control limits covering the 95% confidence interval.**(b) Hypothesis testing**

The average age of employees at Sturt Ltd is 42. In a retrenchment, 49 persons were laid-off. Their mean age was 45. The Equal Opportunity Commission claimed that Sturt was guilty of age discrimination because it had laid-off older than average workers.

Is the information sufficient evidence to support the claim of age discrimination if o (sigma) = 10.8 years? Use a = 0.05.

1. Show the null and alternative hypotheses.

2. Calculate the critical value (actual value or Z-value)

3. Sketch the situation, showing the critical value and the reject region (in terms of actual values or Z-values).

4. Explain your conclusion