The photoresist thickness in semiconductor manufacturing has mean of 15 micrometers and standard deviation of 1 micrometer. Suppose that the thickness is normally distributed and that thicknesses of different wafers are independent.
i. Determine the probability that the average thickness of 5 wafers is either greater than 16 or less than 14 micrometers.
ii. Determine the number of wafers that need to be measured such that the probability that the average thickness exceeds 16 micrometers is 0.01.
iii. If the mean thickness is 15 micrometers, what should the standard deviation of thickness equal so that the probability that the average thickness of 15 wafers is either more than 16 or less than 14 micrometers is 0.001?