please answer all these question

(a) A technical report has the following summary information for fracture strength (in MPa) of n = 169 ceramic bars fired in a particular kiln: x = 89.10, s = 3.73. (i) Using a confidence level of 95%, calculate a two-side confidence interval for true average fracture strength. Then justify whether it appears that the average fracture strength has been precisely estimated. (5 marks) (ii) Suppose the investigators had believed a priori that the population standard deviation was about 4 MPa. Based on this supposition, assume how large a sample would have been required to estimate u to within 0.5 MPa. Use a confidence level of 95%