Central Limit Theorem, Confidence Intervals, Hypothesis Testing

Jul 28th, 2016
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This Document consist of about 10 solved problems of stats as mentioned above... glimpse of few questions are as follows 1) The scores of students taking the ACT college entrance examination are normally distributed with a mean  = 20.1 and a standard deviation  = 2.8. a) A SRS of 12 students are selected at random. Determine the probability that their mean ACT score was between 19.5 and 21.9. b) A SRS of 25 students are selected at random. Determine the probability that their mean ACT score was at least 21.3. 2) To estimate the mean size of maple trees in a certain area of the Adirondacks. A sample of 15 maple tree heights is collected (assume population tree heights is normally distributed). 38 47 28 42 32 38 34 45 40 24 37 49 38 47 47 a) Create a 95% confidence interval for the population mean of maple tree heights. b) Create a 98% confidence interval for the population mean of maple tree heights. c) What size sample would you need to estimate the population

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1Directions Please show all work on exam. If you need to use scrap please label the scrapto indicate the question you are working on. Good luck.PART 1: Central Limit Theorem (#1)1) The scores of students taking the ACT college entrance examination are normallydistributed with a mean = 20.1 and a standard deviation = 2.8.a) A SRS of 12 students are selected at random. Determine the probability that their meanACT score was between 19.5 and 21.9.Z score for score 19.5 :P(Z<19.5) = 0.4152 (from table)Z score for score 21.9:P(Z<21.9) = 0.7389 (from table)Therefore P (19.5

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