Question 3 A second-hand car dealer has 10 cars for sale. They decide to investigate the link between the age of the cars, x and the mileage, y thousands miles. The data collected from the cars are shown in the table below: 60 6.5 30 58 58 Age 2 2.5 3 4 4.5 4.5 5 3 X Mileage y 22 34 == 33 37 40 45 49 50 + Ex=41 =406 =188 xy=1818.5 Zy=17752 a) Find Sxx, Sxy and Syy (6 marks) b) Find the product moment correlation coefficient between x and y c) Find coefficient of determination (2 marks) (2 marks) d) Find the equation of the least squares regression line in the form = a + x. Give the values of a and to 2 decimal places. (6 marks) e) Draw a simple graph and give a practical interpretation of the slope b (2 marks) f) Use your answer to part b), find the mileage predicted by the regression line for a 5 years old car. Question 4 (2 marks) The weights of adult male Siamese cats are known to follow a normal distribution with a mean of 4.5 kg and a standard deviation of 0.8 kg. a) Calculate the probability that a randomly selected cat weighs less than 4 kg. (2 marks) b) Calculate the probability that a randomly selected cat weighs between 3.5 kg and 5 kg. (2 marks) c) Calculate the probability that 45 randomly selected cats have a mean weight lower than 4.4 kg. (3 marks) d) What is the weight of the lightest cat in the top 33%? (3 marks)