# A manufacturer of pharmaceutical products analyses each batch of a product to verify the concentration of the active ingredient. The chemical

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Question: confidence interval for mean

A manufacturer of pharmaceutical products analyses 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 = 0.0076 grams per litter. Three analyses of one batch give concentrations 0.8412, 0.8307, and 0.8321 g/l. To estimate the true concentration, give a 95% confidence interval for μ. (Round your answers to four decimal places.)

Given: the concentration of the active ingredient follows a Normal distribution with mean μ equal to the true concentration and standard deviation σ = 0.0076 grams per litter.

We have to find 95% confidence interval for mean μ.

Formula for confidence interval for mean μ is given by:

$(\bar{x}-E\:&space;\:&space;<&space;\mu&space;<&space;\:&space;\:\bar{x}+E&space;)$

…………