(ii) Suppose an estimate is needed for the average coating thickness for a population of 1,000 circuit boards received from a supplier. Rather than measure the coating thickness on all 1,000 boards, one might randomly select a sample of 36 for measurement. Suppose that the average coating thickness on these 36 boards is 0.08mm and the standard deviation of the 36 coating measurements is 0.013mm. The standard deviation is assumed known from past experience. Determine the 95% confidence interval for the true mean (Note: Relevant Confidence Interval Formulae are in the Formulae pack on page 5) (3 marks) The diameter of a batch of turned shafts is normally distributed with = 2.015cm and =0.0053cm. The customer specification is 2.01250.0125cm (1) Compute the Cpk value and comment on its meaning (3 marks) (2) Determine algebraically whether the process is exhibiting excessive variation. (3 marks) (3) Determine in parts per million (PPM's) the proportion of units (if any) outside specification (5 marks) (4) If the batch described in 2 (b) is representative of the overall process performance, estimate the Sigma level of the process. (Note: Distribution Tables are in the Formulae Pack on pages 11 to 13) (4 marks)