Question

3.25. The following method was proposed to estimate the number of people over the age of 50 who reside in a town of known population 100,000: "As you walk along the streets, keep a running count of the percentage of people you encounter who are over $50 .$ Do this for a few days; then multiply the percentage you obtain by 100,000 to obtain the estimate." Comment on this method. Hint: Let $p$ denote the proportion of people in the town who are over $50 .$ Furthermore, let $\alpha_{1}$ denote the proportion of time that a person under the age of 50 spends in the streets, and let $\alpha_{2}$ be the corresponding value for those over $50 .$ What quantity does the method suggested estimate? When is the estimate approximately equal to $p ?$

          3.25. The following method was proposed to estimate the number of people over the age of 50 who reside in a town of known population 100,000: "As you walk along the streets, keep a running count of the percentage of people you encounter who are over $50 .$ Do this for a few days; then multiply the percentage you obtain by 100,000 to obtain the estimate." Comment on this method.

Hint: Let $p$ denote the proportion of people in the town who are over $50 .$ Furthermore, let $\alpha_{1}$ denote the proportion of time that a person under the age of 50 spends in the streets, and let $\alpha_{2}$ be the corresponding value for those over $50 .$ What quantity does the method suggested estimate? When is the estimate approximately equal to $p ?$

Added by Sean T.

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