What's the distribution of x̅ ?

Question

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 143 minutes with a standard deviation of 14 minutes. Consider 49 of the races.

Let X = the average of the 49 races.

 

How do I write the distribution of x̅ ? I also have to round the standard deviation to two decimal places

I think it's x̅ ~ N (143, ???)

Answer 1

The standard deviation of the mean is the standard deviation/square root sample size = 14/7 = 2. N(143,2).