At a light bulb factory, 1728 light bulbs are 9. ready to be packaged. A work er

Question

At a light bulb factory, 1728 light bulbs are 9. ready to be packaged. A work er randomly pulls 60 light bulbs out and tests each one. Two light bulbs are found to be defective a. Based on the information given, what is your t estimate for the number of defective light bulbs among the 1728 light bulbs? Explain your reasoning. b. If the light bulbs are put in boxes with 144 light bulbs in each box (in 12 packages of 12), then approximately how many defective light bulbs would you expect to find in a box? Ex- plain your reasoning.

Explanation / Answer

Total light bulbs to be packaged = 1728

sample size = 60

defective bulbs = 2

Probability of finding a defective bulb in a sample = 2/60 = 1/30

p^ = 1/30

(a) So as we predict that population estimate p = sample estimate p^

so proortion of bulb which are defectives are = 1/30

so expected number of bulbs that are defecrive = 1728 * 1/30 = 57.6 bulbs

(b) Similarly, for each box the proportion of bulbs that can be defective is equal to sample estimated

so here also deffective light bulbs in each box = 144 * (1/30) = 4.8 bulbs

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