Answer :
Final answer:
The population mean, μ, represents the mean of all 135 swimmers' times in this context. Although the sample of 57 swimmers is used to estimate this mean, it does not define the total population size that the mean is calculated from.
Explanation:
In statistics, when we discuss about a population mean, μ, we are referring to the mean of the entire population, not just a sample of it. In this instance, the population comprises all the 135 swimmers. Therefore, the mean of μ denotes the average of all 135 swimmers' times, not just the 57 in the sample.
So, the correct answer to the question, 'If a sample of 57 swimmers is taken from a population of 135 swimmers, the population mean, μ, is the mean of how many swimmers’ times?' is option B, 135.
A caveat, however, is that while you might have data from a sample of 57 swimmers, this does not give you a precise measurement of the population mean - you are estimating it based on the sample. This is because the sample mean is an unbiased estimator of the population mean, meaning that on average, the sample mean is equal to the population mean, but this might not always be the case for a specific sample.
Learn more about Population Mean here:
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