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Instructions: 1.There are 5 questions 2. Students are required to cover all stated requirements. 3. Your answer must be both in microsoft word file and handed over a printed copy. 4. You need to support your answers with appropriate Harvard style references where necessary. QUESTIONS Question 1: (4 marks) A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30. Compute the following measures: a) Compute the sample mean (the average of the points of each game) (1 mark) b) Compute the sample median (1 mark) c) Compute the variance and the standard deviation (2 marks) Question 2: (6 marks) Suppose during weekends, 55 percent of adults go to the beach, 45 percent go to the cinema, and 10 percent go to both the beach and the cinema. a) What is the probability that a randomly chosen adult does not go to the cinema? (2 marks) b) What is the probability that a randomly chosen adult go to the beach or the cinema or both? (2 marks) c) What is the probability that a randomly chosen adult doesn`t go to the beach or the cinema? (2 marks) Question 3: (6 marks) A Financial Consultant has classified his clients according to their gender and the composition of their investment portfolio (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table: Portfolio Composition Gender Bonds Stocks Balanced Male 0.18 0.20 0.25 Female 0.12 0.10 0.15 One client is selected at random, and two events A and B are defined as follows: A: The client selected is male. B: The client selected has a balanced portfolio. Find the following probabilities: a) P(A) (1 mark) b) P(B) (1 mark) c) P(A and B) (1 mark) d) P(A or B) (1 mark) e) P(A/B) (1 mark) f) P(B/A) (1 mark) 2 Question 4: (6 marks) Find the following probabilities by checking the z table a) P(-1.52 < Z < 0.7) b) P((1.15 < Z < 2.45) c) P(-0.9 < Z < -0.3) Question 5: (8 marks) The foreman of a bottling plant has observed that the amount of soda in each “32-ounce” bottle is actually a normally distributed random variable, with a mean of 32.2 ounces and a standard deviation of 0.3 ounce. a) If a customer buys one bottle, what is the probability that the bottle will contain more than 32 ounces? (3 marks) b) If a customer buys a carton of four bottles, what is the probability that the mean amount of the four bottles will be greater than 32 ounces? (5 marks)