Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. Complete the distributions. (Enter exact numbers as integers, fractions, or decimals.) ( a ) X ~ ? v ( b ) * ~ ? vCoal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 61 tons of coal into each oar. The actual weights of coal loaded into each car are normally distributed, with mean u = 61 tons and standard deviation 0 = 1 ton. Ia USE SALT (a) What is the probability that one car chosen at random will have less than 60.5 tons of coal? (Round your answer to four decimal places.) |:| (b) What is the probability that 41 cars chosen at random will have a mean load weight :r of less than 50.5 tons of coal? (Round your answer to four decimal places.) |:| (c) Suppose the weight of coal in one car was less than 60.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? 0 Yes 0 No Suppose the weight of coal in 41 cars selected at random had an average of less than 60.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? 0 Yes, the probability that this deviation is random is very small. 0 Yes, the probability that this deviation is random is very large. 0 No, the probability that this deviation is random is very small. 0 No, the probability that this deviation is random is very large. Suppose x has a distribution with u = 18 and o = 12. LA USE SALT (a) If a random sample of size n = 44 is drawn, find , o and P(18 E x $ 20). (Round ox to two decimal places and the probability to four decimal places.) My = P(18