The average lifetime of a car tire is 20,000 km with a standard deviation of 4,640 km. A random sample of 100 tires is taken for quality control inspection. a) What is the mean of the sample mean? (1 mark) b) Compute the standard error of the sample mean? (2 marks) c) Is the sampling distribution of this sample mean approximately normal? Justify your answer. (2 marks) d) What sample size of car tire is required to provide a 0.96 probability that the average lifetime in the sample will be less than 20,500 km? (7 marks)