A sample proportion is the fraction of a sampled group with a given trait. If the sample was chosen by chance and the question asks about the whole group, find that fraction in Desmos, then apply it to the whole population. Use the sample size as the fraction’s denominator, not the population size.
Hints
- Hint 1
The sample proportion is the share of checked books that are science fiction. The 12 science-fiction titles are part of the 40 checked books, not a count taken from all 1,200. What fraction of the sample are they?
- Hint 2
A random sample is chosen by chance, so its share can estimate the library’s share. Once you know the sample percent, apply it to all 1,200 books, not to the 40 books already checked.
Step-by-step
Apply the sample’s share to the library
Step 1Write the fraction of the sample
The sample is the 40 books checked, and 12 of those are science fiction. So the science-fiction fraction of the sample is . Use 40 as the denominator because only 40 books were checked.
- Step 2
Find the sample percent
Type in Desmos. It displays , meaning 30% of the sampled books are science fiction. A percent is a share out of 100.
- Step 3
Use that share to estimate the whole library
Because the books were picked randomly (by chance) from the library, their share can estimate the library’s share. Apply the sample’s share to all 1,200 books: . Here is the estimated number of science-fiction books, not an exact count.
- Step 4
Calculate the estimated count
Type in Desmos. It returns , so the best estimate is 360 science-fiction books in the library. Choice C.