Question 3 [20 marks] (a) The mean wage for all 5000 employees who work at a large company is RM21.50 per hour and the standard deviation is RM3.50 per hour Let be the mean wage per hour for a random sample of certain employees selected from this company. Find the mean and standard deviation of for a sample size of 150. (3 marks) (b) A sample of 1500 homes sold recently in a state gave the mean price of homes equal to RM344,750. The population standard deviation of the prices of homes in this state is RM63,150. Construct a 99% confidence interval for the mean price of all homes in this state (7 marks) (c) A random sample of eleven packages was selected from a machine packaging sugar in packages marked 1kg. The actual weights of sugar in kg were: 1.01 1.05 1.03 1.07 0.98 0.99 1.04 1.01 1.05 0.99 1.04 Assuming that the weights are normally distributed, calculate a 95% confidence interval for the mean weight of sugar in packages marked 1kg. (10 marks) Question 4 [20 marks]