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The figure below plots the sampling distribution of the mean from 200 samples of size 9 from the population of 1,000 birthweights. The mean of the 1,000 birthweights is 112.0 oz with standard deviation 20.6 oz. The data are available in SALT. 15 14 13 - 12 11 10 9 of samples with birth weight 1 100 130 110 120 Birthweight in oz

(a) If the central-limit theorem holds, what proportion of the sample means should fall within 0.5 lb of the population mean (112.0 oz)? (Round your answer to four decimal places.) 0558 (b) If the centrat-limit theorem holds, what proportion of the sample means should fall within 1 b of the population mean (112.00z)? (Round your answer to four decimal places. () Compare your results in (a) and (b) with the actual proportion of sample means that fall in those ranges. (Use the finering capabilities in SALTS data set page to find the actual proportion of sample means that fall in these ranges.) The actual proportion of averages that fall within 0.5 lb of the population mean (112.0 oz) is This value is --Select- the value found using the central limit theorem. The actual proportion of averages that fall within 1 lb of the population mean (112.0 oz) is This value is Select the value found using the central limit theorem.