Anew production process has been adopted for ub company that manufactures brushings. historical data suggest that these brushing diameter is normally distributed with a standard deviation of 1mm. it is believed that the modification has not affected the shape of the distribution or the standard deviation, but the value of the mean diameter may have changed. a sample of 25 housing units is selected and hole diameter is 6.45. (a) calculate a confidence interval for true average hole diameter using a confidence level of 90%. (b) a processor engineer believes that the confidence interval derived from (a) is too large for quality control. he/she wishes to derive a confidence interval at 90% confidence level that is smaller than 0.1mm. what should his/her sample size be? provide the smallest possible sample size to achieve 0.1mm confidence interval.