Quality Control Simulator

Pre-Algebra · Axiom Academy

LESSON Quality Control & Sampling Why a factory tests a few hundred phones instead of all ten thousand — and how one rate scales to predict the whole batch. 1. Test a Sample, Not the Whole Batch A full day's run is 10,000 phones . Checking all of them is too slow, so we pull a sample — a smaller handful drawn from the batch — and inspect just those. In the animation, a sample of 500 is lifted out of the full run; whatever fraction of the sample is faulty becomes our estimate for the whole. The sample is a small stand-in for the batch Testing the 500-phone sample turns up 50 defective phones. A raw count of 50 only means something next to the 500 we checked, so we write it as a rate — defective over total — then simplify. The animation groups the 500 into tens: in each group of 10, exactly one is faulty, so the rate collapses to 1 in 10 . Same rate, three ways to write it — divide top and bottom by 50. About 1 phone in every 10 is defective. 3. Scale the Rate Up to 10,000 Here is the payoff. If the same 1-in-10 rate holds across the whole run, it must hold for all 10,000 phones. The animation stacks the full batch as 10 equal blocks of 1,000; one in every ten phones is faulty, so a full tenth — one whole block — fills in red. That block is 1,000 defective phones. Shortcut with the percent: of — the same answer, found by multiplying the rate by the batch size. The 1-in-10 rate comes straight from counting. 10,000 total · ~1,000 defective

This is the written version of the interactive lesson above. See the full Pre-Algebra course.