A random survey gives a sample proportion: the fraction of surveyed households with a trait. Divide the number with the trait by the sample size, then use Desmos to take that percent of the whole population. A sample-based count is an estimate, not an exact census count. Even a random sample can differ from the whole town.
Hints
- Hint 1
A sample proportion is the part of the surveyed group with the trait. Divide the households reporting gardens by all households surveyed, not by the town’s entire population. What percent does that give?
- Hint 2
A random sample is picked by chance from the town, so its percent can estimate the town’s percent. Take that percent of all town households, but don’t treat the result as an exact count.
Step-by-step
Scale the sample proportion to the town
Step 1Find the sample proportion
The households reporting gardens are part of the surveyed, so the sample proportion, or fraction of surveyed households with gardens, is . Type in Desmos; it shows , or . Don’t divide by here: that’s the whole town, not the surveyed group.
- Step 2
Decide what the sample can tell you
The households were chosen at random from the town, so random sampling lets the sample’s estimate the percent for the whole town. It doesn’t reveal the town’s exact count.
- Step 3
Estimate the number of town households
Apply to the town’s households. Type below the first line in Desmos; it returns . Because this comes from a survey rather than a count of every household, the best estimate is households with backyard vegetable gardens. Choice C.