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# Confidence Interval

Radiation of microwave ovens has normal distribution with standard deviation ? =0. 6. A sample of 25 microwave ovens produced X = 0. 11. Determine a 95% confidence interval for the mean radiation. Solution : The population is normal, and the observed value X = 0. 11. (0. 11 ? 1. 96 ? 0. 6/v25, 0. 11 + 1. 96 ? 0. 6/v25) = (?. 1252, 3452) is a 95% confidence interval for ?. Q5.

A manufacturer of pharmaceutical products analyzes a specimen from each batch of a product to verify the concentration of the active ingredient. The chemical analysis is not perfectly precise. Repeated measurements on the same specimen give slightly different results.

The results of repeated measurements follow a normal distribution quite closely. The analysis procedure has no bias, so the mean ? of the population of all measurements is the true concentration in the specimen. The standard deviation of this distribution is known to be ? = . 0068 grams per liter.

The laboratory analyzes each specimen three times and reports the mean result. Three analyses of one specimen give concentrations 0. 84030. 83630. 8447. We want a 99% confidence interval for the true concentration ?. The sample mean of the three readings is