A manufacturer of 10 mm diameter ball bearings uses a process which, when operating properly, is calibrated to produce ball bearings with mean diameter μ = 10.00 mm and standard deviation σ = 0.10 mm. In order to evaluate the performance of the process at a particular point in time, a random sample of n ball bearings is to be taken and the diameters determined in a quality control laboratory. Determine the sample size n such that P (10.00 - 1.96σX¯ ≤ X¯ ≤ 10.00 + 1.96σX¯ ) = 0.05 where σX¯ is the standard deviation of the sample mean, X¯ . State whatever assump- tions you may have to make in answering this question.