Amanufacturer of pharmaceutical products analyzes each batch of a product to verify the concentration of the active ingredient. the chemical analysis is not perfectly precise. in fact, repeated measurements follow a normal distribution with mean μ equal to the true concentration and standard deviation σ = 0.0067 grams per liter. three analyses of one batch give concentrations 0.8225, 0.8737, and 0.91 grams per liter.

the mean (±0.0001) of the measurements is .

the 95% confidence interval for μ (±0.0001) is .

2.

a laboratory scale is known to have a standard deviation of σ = 0.00103 grams in repeated weighings. scale readings in repeated weighings are normally distributed, with mean equal to the true weight of the specimen. three weighings of a specimen on the scale give (in grams) 3.414, 3.419, and 3.415.

the 95% confidence interval for the true weight is ± (±0.1).