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A Performance Assessment A bottling machine is operating with a standard deviation of 0.12 ounce. Suppose that in an SRS of 36 bottles, the machine inserted an average of 16.1 ounces into each bottle. Determine a 95% confidence interval for the mean number of ounces in all the bottles this machine fills in one day. Solution: (1) Parameter: we are looking for an estimate of . given σ = 0.12 _ given x = 16.1 (2) Conditions: I – Independent: The population of bottles is sufficiently greater than 10x the sample size. N > 10n R- Random: we are told that the sample is random O –Outliers: no reason to suggest that there are any outliers N – Normal: nothing to indicate skewness S - sample size is sufficiently large n > 30. (3) Calculations: Identify by name or by formula: _ Confidence interval on x where σ is known. OR: x z * n 0.12 = 16.1 + 0.0392 36 = 16.1 + 1.96 (4) I am 95% confident that the true mean number of ounces in a bottle for a particular day is between 16.061 and 16.139 oz