The finishing times, in minutes, for running marathons have an unknown distribution with mean 297 and standard deviation 32 minutes. A sample, with size n=41, was randomly drawn from the population. Using the Central Limit Theorem for Means, what is the mean for the sample mean distribution?

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Answer:

The mean for the sample mean distribution is 297 minutes.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex].

Using the Central Limit Theorem for Means, what is the mean for the sample mean distribution?

The mean is the same as the population mean, that is, 297 minutes.