# What is the probability of there being 6 heads and 4 tails (in any order)?

Student ID Number:

Examination Date:

Module Name: Statistics

Module Code: FC301

FC301 Statistics Practice EOM exam VERSION 1 Page 1 of 10

FC301 Statistics

Questions-End of Module PRACTICE Exam

Time: 120 Minutes

Instructions to students:

1. This is an open book exam; therefore, you need to provide Formula sheet and Normal Z

table.

2. The â€˜open-bookâ€™ means you can access module learning resources, including your textbooks and

notes, whilst you are answering the examination questions. The questions will not ask you to

copy any specific information from your learning materials, rather you will be asked to use the

information and apply it in a thoughtful way.

3. Read all instructions very carefully.

4. At the start of the examination, you need to be able to see/download the question book in pdf

format or Microsoft word format.

5. You are expected to work on this assessment on your own. Please note that you may be required

to attend an online meeting with your teacher to confirm that it is your own work.

6. There are 9 questions in your final paper. You should attempt to answer all questions.

7. In order to complete this assessment successfully you must:

â€¢ Write your Student ID (Pxxxxxx) and your name at the top of each page.

â€¢ Write in black or blue ink. Use pencil for drawing graph only.

â€¢ Show your work fully for each question. You must write a proper use of formula, all

â€¢ Indicate each question and part(s) of a question.

â€¢ Cross out any mistakes.

â€¢ The submission link will close exactly an hour after duration of the exam.

â€¢ Please save the PDF file following this format: <FC301- First name, Last name,

Pxxxxxx>

Good Luck!

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 2 of 10

Revision from the Progress test and final exam topics

Q1. Look at the Stem and Leaf diagram below. What will the median be?

Stem Leaf

3 5 5 5

4 5

5 0 0 0 0 0

6 2 2

7 5

8 0 1 1 1

9 5

a) 50

b) 62

c) 0

d) 75

(1 mark)

Q2. Which of the following can be used in order to calculate the position of the median?

a) 1 = +1

4

b) 2 = 2(+1)

4

c) 3 = 2(+1)

4

d) â„Ž .

(1 mark)

Q3. For a set of data, variance is calculated as 169. What will the standard deviation be?

a) 169

b) 13

c) 14

d) 12

(1 mark)

Q4. Which statistical measure compares the degree of variation from one data series to another?

a) Range.

b) Inter-Quartile Range.

c) Coefficient of variation.

d) Lower Quartile.

(1 mark)

Key: 3|6 means

36

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 3 of 10

Q5. The histogram shows information about the weight of some batteries.

The total number of batteries is:

a) 11

b) 15

c) 32

d) 40

(1 mark)

Q6. Find the Modal Class of the Frequency Table below:

Class Frequency

10 < â‰¤ 20 18

20 < â‰¤ 30 5

30 < â‰¤ 40 29

40 < â‰¤ 50 111

50 < â‰¤ 60 57

60 < â‰¤ 70 3

a) 20 < â‰¤ 30

b) 30 < â‰¤ 40

c) 40 < â‰¤ 50

d) 50 < â‰¤ 60

(1 mark)

Q7. Which of the following is an example of quantitative discrete data?

a) Human blood type (A, B, AB, or O).

b) Worldâ€™s highest waterfalls.

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 4 of 10

c) A baby weighs 3.5 kilograms.

d) Number of actions.

(1 mark)

Q8. The mean is:

e) The sum of all the scores divided by the number of scores.

f) The most frequently occurring score.

g) The frequency of the most common score divided by the total number of scores.

h) The middle score after all of the scores have been ranked.

(1 mark)

Q9. Find the mean of the following set of numbers:

5.6 6.2 0.9 1.4 7.6 39.9

a) 5.29

b) 12.6

c) 10.27

d) 14.83

(1 mark)

Q10. A researcher found out that there is a moderate positive correlation between x and y variables,

with = 0.3. What would the coefficient of determination be?

a) 0.3

b) 0.09

c) 0.9

d) 1

(1 mark)

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 5 of 10

Revision from the final exam topics only

Q11.

a) The university housing office has separate lists of dormitory residents by class level. The

number of dormitory residents in each class level is as follows.

Class level Number of

dorm

residents

Freshman 780

Sophomore 462

Junior 210

Senior 48

Use the table to design a procedure for obtaining a stratified sample of 49 dormitory residents.

Class level Number of

dorm

residents

Freshman

Sophomore

Junior

Senior

(6 marks)

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 6 of 10

b) Put a cross in the box to identify the type of data.

Qualitative Quantitative

Nominal Ordinal Discrete Continuous

Job role (manager, director,

etc.)

Type of chair

Number of light bulbs

Position in a tournament

Blood pressure

(5 marks)

(TOTAL of 11 marks)

Q12. The following set of data shows the hours of studying per week (x) and hours watching television

per week (y) of a sample of people:

Hours studying per week

(x)

Hours watching tv per week

(y)

8 2

7 7

6 12

5 13

2 13

a) Draw a scatter diagram on the graph paper provided to represent these data.

You cannot use Excel or other online programs to draw your graph. It must be hand drawing

(5 marks)

b) Calculate Pearsonâ€™s moment correlation coefficient.

(4 marks)

c) Interpret Pearsonâ€™s moment correlation coefficient.

(2 marks)

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 7 of 10

d) Write the equation of the regression line of y on x.

(2 marks)

e) Draw the regression line on your scatter diagram.

(1 marks)

f) Interpret the slope of the regression line.

(1 mark)

g) Calculate the coefficient of determination.

(1 mark)

h) Interpret the coefficient of determination.

(1 mark)

i) Use the equation of the regression line to estimate y, when x is 12.

(1 mark)

(TOTAL of 18 marks)

Q13. The table below shows quarterly data for % part-time unemployment:

Year Quarter

I II III IV

2000 4.8 4.5 3.2 3.5

2001 4.9 3.6 2 2.7

2002 4.1 3.4 1.8 1.8

a) On the graph paper provided, draw and label a Time Series graph to show the above data.

You cannot use Excel or other online programs to draw your graph. It must be hand drawing

(5 marks)

b) Calculate the moving average figures from the above table.

At least show three calculations for finding MA (4 marks)

c) Plot the centered moving averages on the Time Series graph and use these points to draw a trend

line. At least show three calculations for finding CMA

(5 marks)

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 8 of 10

d) Use your trend line to predict the unemployment rate (%) in Quarter 1 2004.

(2 marks)

(TOTAL of 16 marks)

Q14. A box of chocolates contains 7 Mars bars, 4 Milky Way, and 2 Twix. Jenny decides to take two chocolate

bars from the box.

i. Construct a tree diagram to show the above information. (3 marks)

ii. What is the probability that Jenny will pick 2 Twix? (2 marks)

iii. What is the probability that Jenny will pick a Milky Way first, and then a Twix? (3 marks)

Q15. There are 25 students in a class, and seven of them are to be (randomly) selected to be on a student committee.

i. In how many ways can this be done? (1 mark)

20 athletes are competing in a race for which there are three prizes, gold, silver, and bronze.

ii. How many possible outcomes are there (assuming no ties)? (1 mark)

Q16. A fair coin, which may land Heads or Tails, is going to be tossed 10 times and the results recorded in order.

i. How many possible outcomes are there? (1 mark)

ii. What is the probability of there being 6 heads and 4 tails (in any order)? (2 marks)

Q17. A discrete random variable has the probability density function () = ( = ), as given in the

following (incomplete) table:

() . . . .

i. Calculate () (2 marks)

ii. Find the expected value, (), (3 marks)

iii. and the variance, () (3 marks)

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 9 of 10

Q18. Given that the set of numbers: . , . , . , . , . , . has âˆ‘ = and âˆ‘ =

i. Find the mean value (2 marks)

ii. And the standard deviation (2 marks)

For the set of numbers: , , , , ,

iii. Find the mean value (2 marks)

iv. and the standard deviation (2 marks)

Q19. A fair, four-sided, spinner is spun 7 times. On any one throw it may land 1, 2, 3, 4, with equal probability.

Calculate the probability that:

i. It lands 1, 3, 4, 2, 1, 1, 3 (in that order, i.e. 1 first, 3 second, 4 third etc.) (2 marks)

ii. The total number of 4s is exactly 2 (3 marks)

iii. The total number of 4s is no less than 2 (2 or more) (4 marks)

Q20. Given that is the standard normal distribution: ~(, ), determine

i. ( < . ) (1 mark)

ii. ( > . ) (2 marks)

iii. (âˆ’. < < . ) (3 marks)

A random variable is normally distributed with mean = and variance =

iv. Calculate the probability (. < < . ) (3 marks)

Student ID number: Student name:

FC301 Statistics Practice EOM exam VERSION 1 Page 10 of 10

Q21. The distribution of heights of adult men in Wales is modelled by the normal distribution, with mean 176cm

and standard deviation 5cm. Measurements of height are recorded to the nearest centimetre. Calculate the

probability that a randomly selected Welsh manâ€™s height is recorded as being:

i. less than 180cm (3 marks)

ii. no more than 180cm (3 marks)

***********************This is the end of the examination paper *************************

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