9. (a) A researcher reports that average salary of assistant professor is more than RM10000. A sample of 35 assistant professors has a mean salary of RM11260. At a =0.05, can you reject the researcher's claim? The standard deviation of the population is RM3240. (7 marks) 6) The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last (1) less than 7 months. (3 marks) (ii) between 8 and 15 months. (3 marks) (c) Based on data from the National Health and Nutrition Examination Survey, assume that weights of men are normally distributed with mean of 98 kg and standard deviation of 25 kg. (1) Find the probability that if an individual man is randomly selected, his weight will be greater than 105 kg. (3 marks) (in) Find the probability that 25 randomly selected men will have a mean weight that is less than 80 kg. (4 marks)