STATISTICS & PROBABILITY QUESTION

QUESTION 5 [20 MARKS] A lm-coating process produces lms Whose thicknesses are normally distributed with a mean of 1 10 microns and a standard deviation of 10 microns. For a certain application, the maximum acceptable thickness is 125 microns. (a) What is the probability that the thickness of a randomly selected lm is between 9'0 microns and 115 microns? [5 Marks] ([3) What is the probability that the thickness of a randomly selected film will be unacceptable? [4 Marks] (0) Ifthe mean remains at 110 microns, what is the value of the standard deviation so that only 5% of the lms will have unacceptable thickness? [6 Marks] (d) lfa sample of 25 lms are selected, nd the probability that the mean thickness of the films is less than 112 microns. [5 Marks]