Statistics Exam

Questions- End of Module SUMMATIVE 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.

1. The ‘open-book’ 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.

1. Read all instructions very carefully.

1. At the start of the examination, you need to be able to see/download the question book in pdf format or Microsoft word format.

1. 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.

1. There are 9 questions in this paper. You should attempt to answer all questions.

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

1. Write your Student ID (Pxxxxxx) and your name at the top of this page.

1. Read the task information carefully before you begin to write.

1. Use clean and A4 paper to Write your answer.

1. Write in black or blue ink. Use pencil for drawing graph only.

1. Show your work fully for each question. You must write a proper use of formula, all the calculation(s) you are doing in your brain or your calculator and a final answer.

1. Your answer must be readable and clear.

1. Number all answer pages at the top of each page.

1. Indicate each question and part(s) of a question.

1. Cross out any mistakes.

1. The submission link will close exactly an hour after duration of the exam.

1. You must submit your answer in pdf format only.

Good Luck!

Statistics EOM exam

0. In a game of chess, a player can either win, draw or lose. The probability that Nihan wins any game of chess is 0.5. The probability that Nihan draws any game of chess is 0.3. Nihan plays 2 games of chess.

a) Construct a tree diagram to show the above information. (5 marks)

b) Work out the probability that Nihan will win both games? (2 marks)

c) Nihan’s friend, Kaisen, said ‘the probability she does not draw in games of chess is 0.39. Is he correct? Explain your answer. (2 marks)

(Total of 9 marks)

2.

a) On a menu in a restaurant there are 6 starters, 5 main courses and 3 desserts to choose from.

i. How many different three-course meals could you have? (1 mark)

ii. In a two-course meal one of the meals has to be a dessert. How many different two-course meals could you have? (1 mark)

b) Yujie has two fair spinners. Spinner A has three equal sections— 2 black and 1 yellow. Spinner B has five equal sections— 3 black and 2 yellow. He spins spinner A, then spinner B.

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

3. The random variable Y has mean 2 and standard deviation of 3. Find:

Hint: Express these in terms of the original and

a) (1 mark)

b) (2 marks)

c) (2 marks)

d) (2 marks)

e) (3 marks)

f) (2 marks)

(Total of 12 marks)

Summary statistics for these data are as follows:

a) Calculate the equation of the linear regression line of on . (7 marks)

b) Calculate the product moment correlation coefficient (3 marks)

c) The coefficient of determination . Give an appropriate comment.

(1 mark)

The equation of the new regression line is:

d) Calculate the estimate for an overall length of 100 metres using this new equation.

(2 marks)

(Total of 13 marks)

5. A fair cubical (six-sided) die is thrown four times. Use the binomial probability formula to calculate:

a) The probability of no threes. (2 marks)

b) The probability of at least 2 threes. (7 marks)

(Total of 9 marks)

6. A college has 3 sports clubs: football, rugby, and basketball. Michael is conducting a stratified sample of sports players at his college. The table below gives some information about the sizes of the groups.

a) Complete the table. (3 marks)

b) A Volleyball sport club has been added to this college. The number of Volleyball players are 120. A new stratified sample of size 60 is required. Calculate the number of each type of sport club that should be chosen. (3 marks)

(Total of 6 marks)

7. The random variable X represents the weight, in grams, of a chocolate bar. It is known that X is Normally distributed with mean 50.7 and variance 0.72. On the wrapper it states that the bar weighs 50 grams.

a) Find the proportion of these chocolate bars that weigh at least 50 grams. (3 marks)

b) A quality control manager wishes to increase this proportion to 95%.

i. Find the required value of the mean if the variance remains unchanged. (4 marks)

ii. Find the required value of the variance if the mean remains unchanged. (2 marks)

(Total of 9 marks)

8. The weights of another type of chocolate bar are also Normally distributed. On the wrapper it states that the bar weighs 25 grams. It is known that 99% of these bars weigh at least 25.0 grams and 75% of them weigh at least 25.4 grams.

a) Find the probability that one of these bars weighs at least 26.0 grams. (6 marks)

b) One bar of the first type (from Q7) and 2 bars of the second type (Q8) are selected at random. Find the probability that at least one of the bars has a weight less than that stated on its wrapper. (2 marks)

(Total of 8 marks)

9. The time series graph gives information about the total amount of money spent by overseas tourists in the UK for each quarter for the years 2011 to 2013.

A trend line has been drawn on the graph. The trend line is based on 4-point moving averages.

a) Explain why 4-point moving averages were chosen. (1 mark)

b) Discuss any seasonal variation shown by the graph. Do not do any calculations.

(2 marks)

c) i. Work out the gradient of the trend line. (2 marks)

ii. Hence, Interpret your answer. (1 mark)

d) Calculate an estimate for the total amount of money spent by overseas tourists for Quarter 1 in 2014. You must show your working. (3 marks)

(Total of 9 marks)

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

Statistics EOM exam VERSION 1