The following data represents the weekly profit ($000) of a sample of 35 cafes in a major Australian city over the first few months of 2021.

13.2

12.3

13.0

16.8

15.1

14.8

18.1

14.1

13.5

20.0

8.1

13.7

19.6

13.2

10.6

25.3

16.0

18.9

23.7

5.4

12.5

22.8

19.0

19.8

6.2

11.1

12.5

22.6

7.5

11.7

21.0

14.9

24.3

11.6

9.2

Part A- Using (5, 10] as your first class, summarize this data by creating a table (set of columns) summarizing the following:

Frequency:

Relative frequency (%):

Cumulative Relative Frequency (%):

Part B -Using your table, how many cafes returned a weekly profit greater than $20,000 butless than or equal to$25,000?

Part C -Using your table, what percentage of cafes returned a weekly profit less than or equal to $25,000?

2

Each trimester a business school offers travel excursions for students, at a small fee. The business school staff would like to survey students about future excursions. Staff have proposed two sampling strategies, listed below.

a) The first sampling strategy is to email a random sample of business school students and ask them to survey about different types of travel excursions.

What type of bias may this suffer from? Briefly explain your choice in the context of this question.

b) The second sampling strategy is to place a "suggestions box" in the student lounge on campus with a sign asking students to offer suggestions for excursions.

What type of bias may this suffer from? Briefly explain your choice in the context of this question.

3 A local council researcher wishes to estimate the proportion of ratepayer residents who are satisfied with the council's budget. To obtain a representative sample of 500 ratepayers, the researcher has proposed the following sampling methods.

a) The first sampling method proposed is to select every tenth ratepayer from an alphabetical listing of the 5000 ratepayers in the council area.Which sampling method was used here AND explain your choice of that sampling method, in the context of this question.

b) The second sampling method proposed is to randomly select one road that has 500 ratepayers and census of all rate payers living on that road.Which sampling method was used here AND explain your choice of that sampling method, in the context of this question.

4 The monthly demand (in thousands) for a particular magazine at a newsagent is listed below along with corresponding probabilities.

Demand (X)

P(X)

1

0.2

2

0.3

3

0.4

4

0.1

Show workings for each of your answers.

Find the expected demand and interpret.

Find the standard deviation of demand.

5 Briefly discuss whether each of the following statements is true or false.

a) The variance of the numbers in a particular data set was small because the numbers themselves were small.

b) Increasing the maximum value of a data set will increase the median value of the data set.

c) A symmetrical distribution must be unimodal.

6

A political candidate with 97909 registered voters in her electorate, wants to survey these voters to ascertainherchance of winning a seat in the next up-coming election.Of the 4939 registered voterswho responded to the survey, it was found that 78% stated that they would vote for her.What is the size of the population?

7 Here is a frequency table of weekly rent ($) paid by students:

Class

Frequency

(0, 120]

17

(120, 240]

16

(240, 360]

13

(360, 480]

11

(480, 600]

19

How many students paid more than $240 per week in rent but less than or equal to $480 per week?Please give your answer with no units.

What proportion of students paid less than or equal to $480 per week in rent?Give your answer as a decimal, to two decimal places, (NOT as a percentage).

8 Here is a sample of data:

3

5

8

4

7

6

What is the value of the median? Give your answer to one decimal place.

9 The following table shows people's ages cross classified against their attitude to proposed new drink driving laws:

Agree

Disagree

Undecided

Under 20 years

22

25

15

20 to 40 years

26

31

18

Over 40 years

36

29

10

What is the probability of randomly selecting one person from this survey who is over 40 years or agrees with the proposed new drink driving laws?Give your answer as a decimal, to two decimal places, (NOT as a percentage).

10 The following table shows people's ages cross classified against their attitude to proposed new drink driving laws:

Agree

Disagree

Undecided

Under 20 years

35

31

8

20 to 40 years

10

49

15

Over 40 years

37

28

14

What is the probability of randomly selecting one person from this survey who agrees with the proposed new drink driving laws?Give your answer as a decimal, to two decimal places, (NOT as a percentage).

11 The following table shows people's ages cross classified against their attitude to proposed new drink driving laws:

Agree

Disagree

Undecided

Under 20 years

22

45

19

20 to 40 years

15

20

5

Over 40 years

27

26

7

What is the probability of randomly selecting one person from this survey who agrees with the proposed new drink driving laws given that they are over 40 years old?Give your answer as a decimal, to two decimal places, (NOT as a percentage).

12 After flipping a fair coin 5 times and getting 3 tails, what is the probability of getting a tail on the next flip? Give your answer to one decimal place.

13 Say, thatA and B are two independent events such that P(A) = 0.54 and P(B) = 0.29.

What is the value of P(A and B)?Give your answer to two decimal places.

14 You are told that A and B are two events, such that P(A) = 0.54 and

P(B) = 0.27, P(A and B) = 0.08

What is the value ofP(B given A)?Give your answer to two decimal places.

15 A cinema sells tickets at three different prices.The manager has estimated the followingdiscrete probability distribution:

X

P(X)

$9

0.3

$14

0.5

$21

0.2

What is the expected value of the ticket price?Please give your answer to two decimal places.Do NOT include units in your answer.

16 You are told that A and B are two events,such that

P(A) = 0.5 ,

P(B) = 0.39,

P(A and B) = 0.06

What is the value ofP(B given A)?Give your answer to two decimal places.

17 An investment opportunity has the following statistics: mean = 97andvariance = 284.

What is the value of the coefficient of variation, inpercentageform.Please give your answer to two decimal places.Do NOT include units in your answer.

18 You are given the following information:

Statistics

Mean

38

Median

41.2

Mode

67

Q1

16

Q3

41

Minimum

6

Maximum

97

What is the value of the interquartile range?

19 Find the variance of this sample of data.

10

14

5

Please give your answer to two decimal places.Do NOT include units in your answer.