Comparing bulb lifespans from back-to-back stems

Comparing bulb lifespans from back-to-back stems

Secondary 2
9 marks
TGM Original Questions

For the probability calculation, each bulb from the specified factory in the stated group is equally likely to be selected.

The lifespans, in hours, of 20 bulbs from Factory A are 320, 330, 330, 340, 350, 350, 360, 370, 380, 390, 410, 420, 430, 440, 450, 460, 470, 480, 500, 520. The lifespans, in hours, of 20 bulbs from Factory B are 340, 350, 360, 370, 380, 390, 410, 430, 450, 450, 450, 470, 490, 510, 530, 550, 570, 590, 610, 630.

  1. Draw a back-to-back stem-and-leaf diagram using hundreds as stems and tens as leaves.[3]
  2. Find the overall mode.[1]
  3. Factory-A bulbs at or below 360 h fail; find the failure percentage.[1]
  4. Find the probability a Factory-B bulb lasts below 470 h.[2]
  5. Which factory lasts longer? Explain.[2]

Solution:

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Answer:(i) See worked solution (ii) \(450\) h (iii) \(35\%\) (iv) \(\frac{11}{20}\) (v) Factory B, with higher median \(450\) h versus \(400\) h.

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