Question 1 (2 marks)

The population mean age of employees in a large company is 42 years with a standard deviation of 5 years. A random sample of 36 employees was found to have a mean age of 38 years with a standard deviation of 6 years. Which of the following statements is correct?

µ= 42 years, s = 6 years, x ¯ = 38 years and s = 5 years.

µ= 38 years, s = 5 years, x ¯ = 42 years and s = 6 years.

µ= 42 years, s = 5 years, x ¯ = 38 years and s = 6 years.

µ= 38 years, s = 5 years, x ¯ = 42 years and s = 6 years.

All of these choices are correct.

Your choice for Question 1:

Briefly explain why you made this choice.

Question 2 (2 marks)

The following is a sample of orders per day, X: 4, 4, 5, 6, 6, 7 ,10

You are given additional information that ?x = 42 and ?x2 = 278.

Which of the following is the sample standard deviation?

a) 1.92 orders per day

b) 2.08 orders per day

c) 2.38 orders per day

d) 4.33 orders per day

e) 2.50 orders per day

Your choice for Question 2:

Show workings to support your answer.

Question 3 (2 marks)

The average price of a litre of unleaded petrol in 2018 was $1.40 and in 2019 was $1.30.

Which of the following is the correct interpretation of the percentage change in petrol price from 2018 to 2019?

There has been a $0.10 decrease in the average price of unleaded petrol from 2018 to 2019.

There has been a $0.10 increase in the average price of unleaded petrol from 2018 to 2019.

There has been a 7.14% decrease in the average price of unleaded petrol from 2018 to 2019.

There has been a 7.69% decrease in the average price of unleaded petrol from 2018 to 2019.

There has been a 92.86% decrease in the average price of unleaded petrol from 2018 to 2019.

Your choice for Question 3:

Show working to support your answer.

Question 4 (2 marks)

An individual has the choice between two investments; an account which pays 0.8% compounded monthly or an account which pays 6% compounded annually.

Which of the following statements best describes which choice is better for the investor?

An account which pays 0.8% compounded monthly has an APR of 10.03% per annum, so is better for the investor.

An account which pays 0.8% compounded monthly has an APR of 9.6% per annum, so is better for the investor.

An account which pays 6% annually is better for the investor here.

An account which pays 6% compounded annually is the same as an account which pays 0.8% compounded monthly.

None of these choices is correct.

Your choice for Question 4:

Show workings to support your answer.

Question 5 (2 marks)

After flipping a fair coin 19 times and the coin landing on heads 19 times, what is the probability of getting a tail on the next coin flip?

0

½

1

19/20=0.95

1-19/20 = 0.05

Your choice for Question 5:

Briefly explain the reason why you made this selection here:

Question 6 (2 marks)

If A and B are 2 events with P(A) = 0.3, P(B) = 0.6 and P(A or B) = 0.5, then which of the following is the value of P(A and B)?

0.8

0.4

0.5

0.1

None of these choices is correct.

Your choice for Question 6:

Show workings to support your answer.

Question 7 (2 marks)

For the standard normal variable, Z which of the following is the value of P(Z 1.96)?

0

0.025

0.50

0.975

1

Your choice for Question 7:

Briefly explain how you found your answer.

Question 8 (2 marks)

A random variable X is normally distributed with a mean of $7 and standard deviation $3. What is the probability that the one randomly selected value lies between $6 and $8?

0.3707

0.6293

0.5

0.6293 - 0.3707 = 0.2586

None of these choices is correct.

Your choice for Question 8:

Show workings to support your answer.

Question 9 (2 marks)

When constructing confidence intervals for the population mean, what happens if the sample size is decreased, all else remaining the same?

The confidence interval will include the population mean less often.

The width of the confidence interval remains the same.

The width of the confidence interval increases.

The width of the confidence interval decreases.

We are more likely to be correct.

Your choice for Question 9:

Briefly explain the reason why you made this selection here:

Question 10 (2 marks)

The manager of a company wants to estimate the population mean time a caller is on hold. She took a random sample of calls and found a 90% confidence interval to be 5.8 µ 25.5 minutes.

Which of the following is a correct interpretation of this confidence interval?

If we took many random samples, 90% of the confidence intervals would be 5.8 µ 25.5 minutes.

There is a 90% probability that a person calling this company will have to wait on hold between 5.8 minutes and 25.5 minutes.

We can say with 90% confidence that the population mean waiting time a caller to this company is on hold lies between 5.8 minutes and 25.5 minutes.

90% of the customers in this sample had to wait between an average of 5.8 minutes and 25.5 minutes.

Almost 100% of callers have to wait between 5.8 minutes and 25.5 minutes on hold.

Your choice for Question 10:

Briefly explain the reason why you made this choice.

Question 11 (5 marks)

The manager of an online store wants to investigate the number of items per order purchased by each customer. A random sample of customer orders was taken and the number of items per order summarized in the table below.

5 2 9 8 3 8 3 1 4

3 9 1 2 1 2 1 2 5

2 3 7 8 7 4 6 2 2

7 5 2 9 6 1 1 4 5

Number of items per order

Show workings, where appropriate, to support your answers in each of the following.

a) Calculate the mean number of items per order.

b) Find the median number of items per order.

c) Find the mode number of items per order.

d) Calculate AND interpret the interquartile range.

e) Would you describe the shape for the distribution of number of items per order as negatively skewed, symmetric or positively skewed? Briefly explain.

Question 12 (5 marks)

Parts a) and b) are unrelated. Both are compulsory.

Show workings to support your answers in each of the following.

a) If $100,000 is invested at an interest rate of 2% compounded per annum, what is the future value of this investment after 10 years?

b) If $800 is invested in a deposit account that pays 1% interest compounded monthly for 6 months, what is the future value of this investment?

Question 13 (5 marks)

The following table summarizes data from a survey on consumer satisfaction with their streaming service.

It assumes that and individual in this survey only had access to one streaming service of either Prime, Netflix or Stan.

Satisfied Unsatisfied Undecided Totals

Prime 10 5 10 25

Netflix 10 10 20 40

Stan 25 5 5 35

Totals 45 20 35 100

Use this table to answer the following questions. Please leave your final answer as a fraction.

a) What is the probability that an individual surveyed was satisfied with their streaming service?

b) What is the probability that an individual surveyed streamed Netflix?

c) What is the probability that an individual surveyed was satisfied with their streaming service and streamed Netflix?

d) What is the probability that an individual surveyed was satisfied with their streaming service given that they streamed Netflix?

Question 14 (5 marks)

The manager of a store wants to estimate the population mean dollar amount spent per purchasing customer. He took a random sample of 49 purchasing customers and found a sample mean of $94.70. Assume that the population standard deviation is known to be $8.50.

Show workings, where appropriate, to support your answers in each of the following.

a) Construct a 95% confidence interval.

b) Interpret your confidence interval.

c) Without doing any additional calculations and given the information as provided above, would the width of a 90% confidence interval be the same, narrower or wider than the width of the 95% interval constructed in part a)? Briefly explain your choice.

The population mean age of employees in a large company is 42 years with a standard deviation of 5 years. A random sample of 36 employees was found to have a mean age of 38 years with a standard deviation of 6 years. Which of the following statements is correct?

µ= 42 years, s = 6 years, x ¯ = 38 years and s = 5 years.

µ= 38 years, s = 5 years, x ¯ = 42 years and s = 6 years.

µ= 42 years, s = 5 years, x ¯ = 38 years and s = 6 years.

µ= 38 years, s = 5 years, x ¯ = 42 years and s = 6 years.

All of these choices are correct.

Your choice for Question 1:

Briefly explain why you made this choice.

Question 2 (2 marks)

The following is a sample of orders per day, X: 4, 4, 5, 6, 6, 7 ,10

You are given additional information that ?x = 42 and ?x2 = 278.

Which of the following is the sample standard deviation?

a) 1.92 orders per day

b) 2.08 orders per day

c) 2.38 orders per day

d) 4.33 orders per day

e) 2.50 orders per day

Your choice for Question 2:

Show workings to support your answer.

Question 3 (2 marks)

The average price of a litre of unleaded petrol in 2018 was $1.40 and in 2019 was $1.30.

Which of the following is the correct interpretation of the percentage change in petrol price from 2018 to 2019?

There has been a $0.10 decrease in the average price of unleaded petrol from 2018 to 2019.

There has been a $0.10 increase in the average price of unleaded petrol from 2018 to 2019.

There has been a 7.14% decrease in the average price of unleaded petrol from 2018 to 2019.

There has been a 7.69% decrease in the average price of unleaded petrol from 2018 to 2019.

There has been a 92.86% decrease in the average price of unleaded petrol from 2018 to 2019.

Your choice for Question 3:

Show working to support your answer.

Question 4 (2 marks)

An individual has the choice between two investments; an account which pays 0.8% compounded monthly or an account which pays 6% compounded annually.

Which of the following statements best describes which choice is better for the investor?

An account which pays 0.8% compounded monthly has an APR of 10.03% per annum, so is better for the investor.

An account which pays 0.8% compounded monthly has an APR of 9.6% per annum, so is better for the investor.

An account which pays 6% annually is better for the investor here.

An account which pays 6% compounded annually is the same as an account which pays 0.8% compounded monthly.

None of these choices is correct.

Your choice for Question 4:

Show workings to support your answer.

Question 5 (2 marks)

After flipping a fair coin 19 times and the coin landing on heads 19 times, what is the probability of getting a tail on the next coin flip?

0

½

1

19/20=0.95

1-19/20 = 0.05

Your choice for Question 5:

Briefly explain the reason why you made this selection here:

Question 6 (2 marks)

If A and B are 2 events with P(A) = 0.3, P(B) = 0.6 and P(A or B) = 0.5, then which of the following is the value of P(A and B)?

0.8

0.4

0.5

0.1

None of these choices is correct.

Your choice for Question 6:

Show workings to support your answer.

Question 7 (2 marks)

For the standard normal variable, Z which of the following is the value of P(Z 1.96)?

0

0.025

0.50

0.975

1

Your choice for Question 7:

Briefly explain how you found your answer.

Question 8 (2 marks)

A random variable X is normally distributed with a mean of $7 and standard deviation $3. What is the probability that the one randomly selected value lies between $6 and $8?

0.3707

0.6293

0.5

0.6293 - 0.3707 = 0.2586

None of these choices is correct.

Your choice for Question 8:

Show workings to support your answer.

Question 9 (2 marks)

When constructing confidence intervals for the population mean, what happens if the sample size is decreased, all else remaining the same?

The confidence interval will include the population mean less often.

The width of the confidence interval remains the same.

The width of the confidence interval increases.

The width of the confidence interval decreases.

We are more likely to be correct.

Your choice for Question 9:

Briefly explain the reason why you made this selection here:

Question 10 (2 marks)

The manager of a company wants to estimate the population mean time a caller is on hold. She took a random sample of calls and found a 90% confidence interval to be 5.8 µ 25.5 minutes.

Which of the following is a correct interpretation of this confidence interval?

If we took many random samples, 90% of the confidence intervals would be 5.8 µ 25.5 minutes.

There is a 90% probability that a person calling this company will have to wait on hold between 5.8 minutes and 25.5 minutes.

We can say with 90% confidence that the population mean waiting time a caller to this company is on hold lies between 5.8 minutes and 25.5 minutes.

90% of the customers in this sample had to wait between an average of 5.8 minutes and 25.5 minutes.

Almost 100% of callers have to wait between 5.8 minutes and 25.5 minutes on hold.

Your choice for Question 10:

Briefly explain the reason why you made this choice.

Question 11 (5 marks)

The manager of an online store wants to investigate the number of items per order purchased by each customer. A random sample of customer orders was taken and the number of items per order summarized in the table below.

5 2 9 8 3 8 3 1 4

3 9 1 2 1 2 1 2 5

2 3 7 8 7 4 6 2 2

7 5 2 9 6 1 1 4 5

Number of items per order

Show workings, where appropriate, to support your answers in each of the following.

a) Calculate the mean number of items per order.

b) Find the median number of items per order.

c) Find the mode number of items per order.

d) Calculate AND interpret the interquartile range.

e) Would you describe the shape for the distribution of number of items per order as negatively skewed, symmetric or positively skewed? Briefly explain.

Question 12 (5 marks)

Parts a) and b) are unrelated. Both are compulsory.

Show workings to support your answers in each of the following.

a) If $100,000 is invested at an interest rate of 2% compounded per annum, what is the future value of this investment after 10 years?

b) If $800 is invested in a deposit account that pays 1% interest compounded monthly for 6 months, what is the future value of this investment?

Question 13 (5 marks)

The following table summarizes data from a survey on consumer satisfaction with their streaming service.

It assumes that and individual in this survey only had access to one streaming service of either Prime, Netflix or Stan.

Satisfied Unsatisfied Undecided Totals

Prime 10 5 10 25

Netflix 10 10 20 40

Stan 25 5 5 35

Totals 45 20 35 100

Use this table to answer the following questions. Please leave your final answer as a fraction.

a) What is the probability that an individual surveyed was satisfied with their streaming service?

b) What is the probability that an individual surveyed streamed Netflix?

c) What is the probability that an individual surveyed was satisfied with their streaming service and streamed Netflix?

d) What is the probability that an individual surveyed was satisfied with their streaming service given that they streamed Netflix?

Question 14 (5 marks)

The manager of a store wants to estimate the population mean dollar amount spent per purchasing customer. He took a random sample of 49 purchasing customers and found a sample mean of $94.70. Assume that the population standard deviation is known to be $8.50.

Show workings, where appropriate, to support your answers in each of the following.

a) Construct a 95% confidence interval.

b) Interpret your confidence interval.

c) Without doing any additional calculations and given the information as provided above, would the width of a 90% confidence interval be the same, narrower or wider than the width of the 95% interval constructed in part a)? Briefly explain your choice.

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