A survey that gives a count out of a randomly selected group calls for a sample proportion: the number with the trait divided by the number surveyed. Evaluate that fraction in Desmos, then take the resulting percent of the whole population to estimate a count. Don't treat the sample size as a percent; it tells you how many were surveyed.
Hints
- Hint 1
A sample proportion compares households with the trait to all households surveyed. Put the subscribers over the 40 surveyed households, not over the whole city. What fraction of the sample subscribed?
- Hint 2
A random sample lets you use its subscriber percentage to estimate the city's subscriber percentage. Once you have that percentage, take it of all 120,000 households, not of the 40 already surveyed.
Step-by-step
Use the sample share to estimate the city count
Step 1Write the sample's subscriber share
Of the 40 surveyed households, 12 subscribed. The sample proportion, or part divided by the group surveyed, is . The denominator is 40 because this fraction describes the sample, not the entire city.
- Step 2
Find the percentage to use for the city
Type in Desmos. It shows , or . Because the households were randomly selected from the city, use the sample's share to estimate the city's share.
- Step 3
Estimate the number of subscribing households
Type on the next line. Desmos shows . The whole is the city's 120,000 households, not the sample's 40. About city households would be expected to subscribe. Choice C.