KBAT Problems
KBAT Problem: A Battery Batch Accept-or-Reject Decision
An original KBAT problem that reads a grouped lifespan distribution off its cumulative frequency curve to decide, with working, whether a supplier's batch should be accepted.
The problem
A supplier tests the lifespan, in hours, of a sample of 200 batteries from one batch, grouped as follows: 0–199 (10 batteries), 200–399 (30), 400–599 (50), 600–799 (70), 800–999 (40). The buyer will only accept the batch if at least 80% of the batteries last more than 600 hours.
Using the cumulative frequency curve (ogive), should the buyer accept this batch? Justify your decision.
Full worked solution
- Understand and set up: Build the cumulative frequency table using upper class boundaries: fewer than 199.5 → 10, fewer than 399.5 → 40, fewer than 599.5 → 90, fewer than 799.5 → 160, fewer than 999.5 → 200. Plotting these against the boundaries gives the ogive.
- Plan and read the ogive: The condition of lasting more than 600 hours is the complement of lasting 600 hours or fewer, which the ogive reads at the boundary 599.5. Reading the ogive there gives a cumulative frequency of 90, so 90 out of 200 batteries lasted 600 hours or less.
- Execute and decide: 90 out of 200 is 45%, so only 100% − 45% = 55% of batteries lasted more than 600 hours. Since 55% is below the required 80%, the batch does not meet the buyer's condition, so the buyer should reject it.
Mark-scheme keywords
- Correct cumulative frequency table with upper boundaries (199.5, 399.5, 599.5, 799.5, 999.5).
- Reading the cumulative frequency at the boundary 599.5 as 90 (from the table or the ogive).
- Converting to a percentage: 90/200 × 100% = 45%, then using the complement to get 55%.
- Comparing 55% against the required 80% correctly.
- A clear decision statement (reject the batch) with a reason, not just a number.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
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