Introduction to expectation
A sample tells you a proportion. Multiply it by the size of the whole population to predict how many. One division and one multiplication.
A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
A librarian samples the collection and finds 510 undamaged, 63 with minor damage and 27 with major damage.
Of the 24,000 books in the collection, how many should be expected to have minor damage? Round to the nearest whole number.
A sample of parts contains 288 good, 36 reworkable and 36 scrap.
Of the 15,000 parts produced, how many should be expected to be reworkable? Round to the nearest whole number.
A sample of library books shows 782 undamaged, 71 minor damage and 42 major damage.
Of 36,500 books, how many should be expected to have minor damage? Round to the nearest whole number, and do not round intermediate calculations.
A quality inspector samples a production run. Of the items checked, 640 passed, 48 had minor faults and 32 had major faults.
Based on this sample, how many of the 18,000 items in the full run should be expected to have minor faults?
The sample size
The proportion
Scale to the run
The shortcut worth seeing
The population is 25 times the sample (18,000 ÷ 720 = 25), so the expected count is just 48 × 25 = 1,200.
That works whenever the numbers divide cleanly, and it avoids the decimal entirely. When they do not divide cleanly, fall back to the proportion — but check first, because ALEKS often chooses numbers that do.