Coal 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 71 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean-71 tons and standard deviation -1.2 ton. USE SALT (a) What is the probability that one car chosen at random will have less than 70.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 21 cars chosen at random will have a mean load weight x of less than 70.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 70.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes O No Suppose the weight of coal in 21 cars selected at random had an average x of less than 70.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this deviation is random is very small. Yes, the probability that this deviation is random is very large. No, the probability that this deviation is random is very small. No, the probability that this deviation is random is very large. Suppose x has a distribution with 14 and -9. USE SALT (a) If a random sample of size n = 42 is drawn, find , and P(14 sxs 16). (Round to two decimal places and the probability to four decimal places.) - - R(145 x 516) - (b) If a random sample of size n = 65 is drawn, find and P(14 sxs 16). (Round to two decimal places and the probability to four decimal places.) 1- P(14 x 16) - (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is-Select- part (a) because of the ---Select- sample size. Therefore, the distribution about is-Select-- Consider an x distribution with standard deviation-48. (a) If specifications for a research project require the standard error of the corresponding x distribution to be 3, how large does the sample size need to be? - (b) If specifications for a research project require the standard error of the corresponding x distribution to be 1, how large does the sample size need to be?