.State the main points of the Central Limit Theorem for a mean..Why is population shape of concern when estimating a mean? What does sample size have to dowith it?.A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477(a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of +_ 0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture..In 1992 the FAA conducted 86991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs and found that 1143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem despite the very small value of p

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