Page 30 - Quality control of pharmaceuticals (07-PA 704)

mg and σ2 = 25. In a random sampling of tablets from the production
line, what percentage are expected to contain between 243 and 262
mg of aspirin?
Solution
We do not determine directly the percentage of tablets between 243 mg
and 262 mg of aspirin.
We calculate the deviation, z, of each limit from µ in terms of the
population’s standard deviation, σ.

Using the table in Appendix 1, we find that the percentage of tablets
between 243 and 250 mg of aspirin is 41.92%, and the percentage
of tablets between 262 and 250 mg of aspirin is 49.18.%. Therefore,
the percentage of tablets containing between 243 and 262 mg of
aspirin is
41.92% + 49.18% = 91.10%

The very fact that we repeat measurements implies that we have more
confidence in the mean of several values than in a single value.
Intuitively we would expect that the more measurements we make,
the more reliable our estimate of μ, the true value, will be.

To pursue this idea, let us return to the nitrate ion determination described
earlier. In practice it would be most unusual to make 50 repeated
measurements in such a case: a more likely number would be 5. We
can see how the means of samples of this size are spread about μ by