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A manufacturer of pharmaceutical products analyzes a specimen from each batch of

ID: 3378922 • Letter: A

Question

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 are known to follow a normal distribution quite closely. The standard deviation of this distribution is known to be s = 0.0068 grams per liter. Management asks the laboratory to produce results accurate to within ±0.005 with 95% confidence. How many measurements must be averaged to comply with this request?

Explanation / Answer

Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 0.0068
ME =0.005
n = ( 1.96*0.0068/0.005) ^2
= (0.0133/0.005 ) ^2
= 7.1054 ~ 8      

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