What would be the X and what would be the Mu in this prob?

[bugmento]

A marathon coordinator has created a new marathon competition where teams composed of
seven runners finish the race and the sample mean time is recorded as their score. The coordinator
hired a statistician to analyze the distribution of these sample means. The path is still the same as in
previous years, and runners averagely finish the path in 74.4 minutes (give or take 26.5 minutes).

If X is the random variable that represents the distribution of these sample mean marathon
times, then this random variable has a mean of
a. 74.4 minutes.
b. 10.63 minutes.
c. 47.9 minutes.
d. 100.9 minutes.
e. 28.12 minutes.

so this would just be A 74.4 right? for the formula Z = (X - Mu) / (Stddev / sqrt(n)), I didn't know what X or Mu were, so I guessed that 74.4 was the value for X (by X i mean X-bar)

Had the coordinator allowed teams to be made up of exactly thirty runners, the value of ?
would
a. increase.
b. decrease.
c. remain constant.
d. None of the above

So this is increasing the value of n from n = 7 to n = 30, so that means the since the sample size increased, the value of Mu (subscript X-bar) would decrease ?


I'm just confused by this problem. Any feedback is very much appreciated. Thanks for reading

 

[markprince77]

The sample mean will remain the same. Mu is unaffected by n, however variance is proportional to 1/n. This can be proved using the Chebyshev inequality

 

[bugmento]

when you say "variance is proportional to 1/n" does that mean as the value of sample size "n" goes up, the value of the standard deviation (subscript x-bar) goes up also? like they are positively correlated?