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 (%):

Frequency

Relative frequency

Cumulative frequency

Relative cumulative frequency

(5,10)

5

14.28%

5

14.28%

(10,15)

15

42.86%

20

57.14%

(15,20)

9

25.72%

29

82.86%

(20,25)

5

14.28%

34

97.14%

(25,30)

1

2.86%

35

100%

Total

35

100%

2. ind the variance of this sample of data.

6

12

3

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

Answer:

3. ou are given the following information:

Statistics

Mean

38

Median

43.8

Mode

72

Q1

21

Q3

42

Minimum

4

Maximum

98

What is the value of the interquartile range?

Answer:

4. n investment opportunity has the following statistics: mean = 135andvariance = 255.

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.

Answer:

5.You are told that A and B are two events,such that

P(A) = 0.49 ,

P(B) = 0.27,

P(A and B) = 0.09

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

Answer:

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

X

P(X)

$8

0.3

$13

0.5

$19

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.

Answer:

7. ou are told that A and B are two events, such that P(A) = 0.41 and

P(B) = 0.38, P(A and B) = 0.09

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

Answer:

8. 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.

Answer:

9. After flipping a fair coin 7 times and getting 0 tails, what is the probability of getting a tail on the next flip? Give your answer to one decimal place.

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

15

22

14

20 to 40 years

34

21

11

Over 40 years

13

35

17

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 apercentage)