1) The average and standard deviation of thickness of a steel plate from 25 samples are measured as 33 mm and 3 mm, respectively. (13 marks) a) If the actual standard deviation thickness is 2 mm, determine the probability of getting a sample standard deviation result as high or higher than 3 mm. Write necessary assumption(s). b) What does your answer of part a imply about the true standard deviation of the thickness being 2 mm? c) How large of a sample is needed to be 96% confident that the sample mean will be within 1 mm of the actual mean, if the actual standard deviation is later confirmed to be 2.5 mm