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##### Coal is carried from mine in VA to a power plant in NY

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**Question**

Question;1.) Coal is carried from mine in VA to a power plant in NY;in hopper cars on a long train. The automatic hopper car loader is set up to;put 36 tons of coal in each car. The actual weights of coal loaded into each;car are normally distributed with a mean (u=36) tons and a standard deviation;(.8 tons). (the u is suppose to be the mean sign and there isn't a standard;deviation sign on my phone);A) What is the probability that ONE car choose at random;will have less than 35.5 tons of coal?;B) What is the probability that 20 card chooses at random;will have a mean load weight (x bar) less than 35.5 tons of coal?;C) Suppose the weight of coal in one car was less than 35.5;tons. Would that fact make you suspect that the loader had slipped out of;adjustment? Suppose the weight of coal in 20 cars deleted at random had an;average of (x bar) less than 35.5 tons. Would that fact make you suspect that;the loader had slipped out of adjustment? Why?;2.) To be licensed as a practical nurse, one must make a;score in the top 30% on the licensing exam. The mean score of all students;taking the exam is 79 with a standard deviation of 9 points and the scores are;given in whole number values. What is the least score a student can make and be;considered in the top 30%?;3.) A certain company makes light fixtures on an assembly;line. An efficiency expert wants to determine the mean time it takes an;employee to assemble the switch on one of these fixtures. A preliminary study;used a random sample of 45 observations and found that the sample standard;deviation was s=78 seconds. How many more observations are necessary for the;efficiency expert to be 95% sure that the point estimate (x bar) will be in the;error from the true mean (u) by at most 15 seconds?

Paper#60963 | Written in 18-Jul-2015

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