Question

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?

Answer 1

The mean for the sample mean distribution is 297 minutes.

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, a large sample size can be approximated to a normal distribution with mean
`\mu` and standard deviation
`(\sigma)/(√(n))`.

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.