Question

Suppose 20% of all widgets produced at a factory are defective. A simulation is used to model widgets randomly selected and then recorded as defective or working. Which simulation best models the scenario? Place 50 equally sized pieces of paper in a hat. Of the 50, 5 read “defective” and the rest read “working”. Place 25 equally sized pieces of paper in a hat. Of the 25, 5 read “defective” and the rest read “working”. Place 20 equally sized pieces of paper in a hat. Of the 20, 5 read “defective” and the rest read “working”. Place 100 equally sized pieces of paper in a hat. Of the 100, 5 read “defective” and the rest read “working”.

Answer 1

Place 25 equally sized pieces of paper in a hat. Of the 25, 5 read “defective” and the rest read “working”.

Answer 2

Percentage of defective widgets = 20% = 0.2
Therefore,
1. 20% of 50 = 0.2*50 = 10 defective widgets
2. 20% of 25 = 0.2*25 = 5 defective widgets
3. 20% of 20 = 0.2*20 = 4 defective widgets
4. 20% of 100 = 0.2*100 = 20 defective widgets.

It can be seen that scenario two 2 best simulates the model. The other three (that is, 1, 3, and 4) scenarios gives wrong answers.