Up until recently, your potato chip factory in Los Angeles was producing chips with an average thickness of 1.35 millimeters (1.35 mm). Recently, new manufacturing equipment was introduced and your customers have suddenly started reporting that the potato chips have gotten thinner. Naturally, you are worried about this, so you arrange to have a random sample of 16 chips taken from the population of all chips produced yesterday. The random sample shows an average thickness of 1.25 mm and a standard deviation of .12 mm. a) Assuming that the thickness of the chips is Normally Distributed, construct a 90% confidence interval for the mean thickness of all chips produced yesterday based upon the sample of size 16. (15 points) b) If the average thickness of all chips is still 1.35 mm, how often would such a confidence interval (a 90% confidence interval based upon a random sample of size 16) fail to contain the number 1.35? Assume that the thickness of the chips is Normally Distributed. (15 points) c) Based upon your answers to parts a) and b), is it believable that the average thickness of all chips is still 1.35 mm? Explain your answer as if you were writing a memo to the CEO of the firm. Assume that the thickness of the chips is Normally Distributed