A sample mean can estimate a stadium total when the sample counts come from equal-sized sections. Find the mean number of hat wearers per section with a Desmos list, then scale it by the number of 200-seat groups in the stadium. Don't scale one unusually low or high section count instead of the mean.
Hints
- Hint 1
The mean is the total of the sample values divided by how many values there are. All six section counts matter, even though the question asks about spectators throughout the stadium.
- Hint 2
Each sampled count describes one 200-seat section. How many groups of 200 seats fit into the stadium's occupied seats? Multiply the sample mean by that number of groups.
Step-by-step
Scale the sample mean
Step 1Find hats per sampled section
The mean is the average of all six section counts. Type in Desmos, then . Desmos shows about , so the sample estimates about hat wearers per 200-seat section.
- Step 2
Count equivalent sections in the stadium
The stadium has occupied seats, and each sampled section has seats. Divide to find how many 200-seat groups the stadium contains: . Scale a sample average by the number of equal-sized groups in the population. Don't multiply by six again; the mean already uses all six sampled sections.
- Step 3
Estimate the total hat wearers
Multiply the mean per section by the 150 equivalent 200-seat groups. Add in Desmos; it shows . That's the estimated total number of spectators wearing hats, which falls in the to range. Choice B.