8.1 Estimation Using Normal

# The be consistent with package labeling boxes should

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Unformatted text preview: be consistent with package labeling, boxes should contain a mean of 368 grams of cereal. Because of the speed of the process, the cereal weight varies from box to box, causing some boxes to be underfilled and others overfilled (the standard deviation is known to be 0.15 grams). If the process is not working properly, the mean weight in the boxes could vary too much from the label weight of 368 grams to be acceptable. Interval Estimation Because weighing every box is too costly, a sample of boxes is selected. The sample is used to decide whether to maintain, alter, or shut down distribution: Population the cereal-filling process. Normal distribution: Mean μ = 368 grams (desired mean) standard deviation σ = 0.15 grams σ Known Example Oxford Cereals fills thousands of boxes of cereal during an 8-hour shift. The be consistent with package labeling, boxes should contain a mean of 368 grams of cereal. Because of the speed of the process, the cereal weight varies from box to box, causing some boxes to be underfilled and others overfilled (the standard deviation is known to be 0.15 grams). If the process is not working properly, the mean weight in the boxes could vary too much from the label weight of 368 grams to be acceptable. Interval Estimation Because weighing every box is too costly, a sample of boxes is selected. The sample is used to decide whether to maintain, alter, or shut down distribution: Population the cereal-filling process. Normal distribution: Mean μ = 368 grams (desired mean) standard deviation σ = 0.15 grams Sampling distribution for Sample Size n = 25: Normal distribution (population follows normal distribution): Mean µ= 6 38 x 5 Standard error of the mean: x = σ = 1 =3 σ n 2 5 σ Known Example Find an interval symmetrically distributed around the population mean that includes 95% of the sample means. Interval Estimation σ Known Example Find an interval symmetrically distributed around the population mean that includes 95% of the sample means. 2.5% xL 95% μ...
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