The amount of aspirin in the analgesic tablets from a particular manufacturer is known to

Question

The amount of aspirin in the analgesic tablets from a particular manufacturer is known to follow a normal distribution, with [latex]\mu=250 ~\mathrm{mg}[/latex] and [latex]\sigma^{2}=25[/latex]. In a random sampling of tablets from the production line, what percentage are expected to contain between 243 and [latex]262 ~\mathrm{mg}[/latex] of aspirin?

Accepted Answer

The normal distribution for this example is shown in Figure 4.7, with the shaded area representing the percentage of tablets containing between 243 and [latex]262~ \mathrm{mg}[/latex] of aspirin. To determine the percentage of tablets between these limits, we first determine the percentage of tablets with less than [latex]243~ \mathrm{mg}[/latex] of aspirin, and the percentage of tablets having more than [latex]262 ~\mathrm{mg}[/latex] of aspirin. This is accomplished by calculating the deviation, [latex]z[/latex], of each limit from [latex]\mu[/latex], using the following equation

[latex]z=\frac{X-\mu}{\sigma}[/latex]

where [latex]X[/latex] is the limit in question, and [latex]\sigma[/latex], the population standard deviation, is 5 . Thus, the deviation for the lower limit is

[latex]z_{ ext {low }}=\frac{243-250}{5}=-1.4[/latex]

and the deviation for the upper limit is

[latex]z_{ ext {up }}=\frac{262-250}{5}=+2.4[/latex]

Using the table in Appendix 1A, we find that the percentage of tablets with less than [latex]243~ \mathrm{mg}[/latex] of aspirin is [latex]8.08 \%[/latex], and the percentage of tablets with more than [latex]262~ \mathrm{mg}[/latex] of aspirin is [latex]0.82 \%[/latex]. The percentage of tablets containing between 243 and [latex]262~ \mathrm{mg}[/latex] of aspirin is therefore

[latex]100.00 \%-8.08 \%-0.82 \%=91.10 \%[/latex]

Question 4.11: The amount of aspirin in the analgesic tablets from a partic...

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