Question

Shana lives in a town with a population of 130,000. Standing outside the largest grocery store, Shana surveyed people to find out how many have cats. Of the people she asked, 106 people had cats and 694 did not. How many cat owners are predicted to live in the town?
There should be 694 cat owners in town.
There should be 1,226 cat owners in town.
There should be 17,225 cat owners in town.
There should be 19,855 cat owners in town.

Answers

GPT-4o mini
To estimate the number of cat owners in the entire town, we can first find the proportion of cat owners in the sample surveyed by Shana.

In her survey, Shana found:
- Cat owners: 106
- Non-cat owners: 694

The total number of people surveyed = 106 + 694 = 800.

The proportion of cat owners in the survey is:
\[
\text{Proportion of cat owners} = \frac{106}{800}
\]

Next, we simplify this fraction:
\[
\text{Proportion of cat owners} = 0.1325
\]

To estimate the total number of cat owners in the town of 130,000 people, we multiply the total population by the proportion of cat owners:
\[
\text{Estimated cat owners} = 130,000 \times 0.1325
\]
\[
\text{Estimated cat owners} = 17,225
\]

Therefore, the predicted number of cat owners in the town is **17,225**.

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