A factory has 30003000 workers, and the probability of randomly selecting a worker who is a part-time employee is 0.250.25. If we want to find the probability of 4040 part-time employees when 100100 workers are randomly selected, are the 100100 selections independent? Can they be treated as being independent using the 5%5\% guideline for cumbersome calculations?

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Problem 52Multiple Choice

A factory has $3000$ workers, and the probability of randomly selecting a worker who is a part-time employee is $0.25$ . If we want to find the probability of $40$ part-time employees when $100$ workers are randomly selected, are the $100$ selections independent? Can they be treated as being independent using the $5 percent sign$ guideline for cumbersome calculations?

No, the selections are not independent, and they cannot be treated as independent because the sample size is too large.

No, the selections are not technically independent, but they can be treated as independent because the sample size is less than $5 percent sign$ of the population.

Yes, the selections are independent because each worker has the same probability of being part-time.

Yes, the selections are independent because the population size is large enough to ignore sampling effects.

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