Question

we are interested in developing a sampling distribution for the average time olympic marathon runners complete a marathon in. this is based on the 2012 mens olympic marathon which had 85 finishers. data is available at statkey, select sampling distribution for a mean, then change the data set to olympic marathon - 2e (minutes).
summary statistics
for samples of size ( n = 10 ) use the standard error formula or create a sampling distribution by running at least 6000 samples based on their data set.
the standard deviation for the population is
the standard error for the distribution of sample means from samples of size 10 is
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Explanation:

Step1: Identify population standard deviation

From the summary statistics table, the standard deviation (StDev) of the population is given as \(8.007\).

Step2: Calculate standard error

The formula for the standard error (\(SE\)) of the sample mean is \(SE=\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.
Given \(\sigma = 8.007\) and \(n = 10\), we have \(SE=\frac{8.007}{\sqrt{10}}\).

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Answer:

The standard deviation for the population is \(8.007\). The standard error for the distribution of sample means from samples of size \(10\) is approximately \(2.532\).