The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with σ = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours. If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence, how many randomly selected 60-watt light bulbs should be tested to achieve this result?

Question

Logan Wilkins

Physics

7 March, 07:42

The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with σ = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours. If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence, how many randomly selected 60-watt light bulbs should be tested to achieve this result?

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Answers (1)

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Leland Moran · Answer 1

They must have about 166 randomly 60 watt light bulbs to achieve the result

N = 166

Explanation:

σ = 30

% 99 = 2.576

Using the standard equation of statistics knowing the difference between the measurement have a margin error no larger than 6 can solve

σ = √∑ (x - z') ² / N

Solve to N

N = (% * σ / Δ x) ²

N = (2.576 * 30 / 6) ²

N = 12.88 ²

N = 165. 89 44 ≅ 166