Final answer:
The question falls within the domain of High School Mathematics and involves calculating the probability of a certain number of defective light bulbs using the Poisson distribution as an approximation.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with the topic of probability and its applications to real-world scenarios. The question would typically be encountered at the High School level, particularly in statistics or advanced algebra courses.
The probability of finding between 31 and 60 defective light bulbs out of 3000, with each bulb having a 0.01 chance of being defective, can be calculated using either the binomial distribution or a normal approximation to the binomial distribution. Since the number of trials is large and the probability of success is small, using the Poisson distribution can be considered a good approximation. Assuming a Poisson distribution, the mean (μ) would be 3000 * 0.01 = 30. To find the probability of having between 31 and 60 defective bulbs, we would essentially calculate P(31 ≤ X ≤ 60).
Although the exact calculation isn't provided, this will typically involve using a Poisson probability table or a statistical software to find the cumulative probability for P(X ≤ 60) and subtract the cumulative probability for P(X < 31).