© 2010 Radha Bose Florida State University Department of Statistics ABC

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CENTRAL LIMIT THEOREM 15/209. Let us suppose that the left eye spherical measurements on eyeglass prescriptions are Normally distributed with mean 0 diopters and standard deviation 1 diopter. We will randomly select 35 people and calculate their mean left eye spherical measurement, . For parts (b)-(d), draw an appropriately shaded and labeled density curve to support your work and include probability notation. Sub: ____________________ Obs: ____________________ Shape: ____________________ (a) Write down the distribution of the sample mean . ________________________________ (b) What is the probability that the sample mean turns out to be less than -0.4 diopters? (c)What is the probability that the sample mean turns out to be within 0.4 diopters of the population mean? (d)What is the 90thpercentile of the sampling distribution of (e)Write out a “percentage of data” interpretation of the picture you drew in each of parts (b) through (d), in words, in context. ? © 2010 Radha Bose Florida State University Department of Statistics

CENTRAL LIMIT THEOREM 16/2010.We wish to know the average number of days that US marine officers spend on assignment in Atlantic waters. We randomly select 150 Atlantic assignments and calculate the average number of days, let us call it P. We then randomly select 120 Atlantic assignments and calculate the average number of days, let us call it Q. Which average, P or Q, is more likely to be closer tothe average for allAtlantic assignments? State P or Q and give a reason for your answer. 11.Let us suppose that the weights of baby elephants are Normally distributed with mean 224 lbs andstandard deviation 53 lbs. Sub: ____________________ Obs: ____________________ Shape: ____________________ (a) What is the probability that the mean weight of 18 randomly selected baby elephants will be more than 245 lbs? (b)Write out a “percentage of data” interpretation of your answer to part (a) in words, in context. (c)What is the probability that a single randomly selected baby elephant will weigh more than 245 lbs? (d)Is it more likely that the weight of a single baby elephant or the mean weight of 18 baby elephantswill be more than 245 lbs? (e)Your answer to part (c) illustrates that © 2010 Radha Bose Florida State University Department of Statistics

CENTRAL LIMIT THEOREM 17/20