https://file.aiquickdraw.com/mathbot/file/17296364013981khmcdkp.jpg

The problem displayed in the image is a proportion problem. Let's break it down:

- A sample of 103 households was taken, and 33 were watching "Town Talk."
- You are asked to estimate how many households, out of 182,000, would be expected to watch "Town Talk."

This is a proportion problem where we use the ratio of viewers in the sample to predict the viewers in the larger population. The proportion can be set up as follows:

\[
\frac{33}{103} = \frac{x}{182,000}
\]

Where:
- 33 is the number of households watching in the sample.
- 103 is the total number of households in the sample.
- \(x\) is the number of households expected to be watching in the population of 182,000.

To solve for \(x\), cross-multiply and solve the equation:

\[
33 \times 182,000 = 103 \times x
\]

\[
x = \frac{33 \times 182,000}{103}
\]

Let me calculate that for you:

\[
x = \frac{33 \times 182,000}{103} = \frac{6,006,000}{103} \approx 58,291.26
\]

So, you would expect approximately **58,291 households** to be watching "Town Talk."

Would you like more details or have any questions?

Here are some related questions to expand on this topic:

1. What is a proportion, and how does it help in real-life estimations like this?
2. How would the result change if the sample size were larger or smaller?
3. What happens if the percentage of viewers changes? How would you recalculate?
4. Can this method of proportion be applied to other types of survey data?
5. How can you improve the accuracy of your estimate in a population survey?

**Tip**: Always double-check your cross-multiplication and division in proportion problems to avoid small errors that could lead to big differences in your results.

A television rating service found that out of a sample of 103 households, 33 were watching Town Talk during its time slot. Suppose there are 182,000 households in a marketing region. How many of them would you expect to be watching Town Talk?

Learn how to estimate the number of households watching 'Town Talk' using proportions. Based on a sample of 103 households with 33 viewers, this problem involves predicting the viewership for a population of 182,000. Key math concepts include proportions, ratios, and cross-multiplication.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation