Answer:
μ = 6500
μx= 6500
σx= 76
σ= 450
n= 35
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average game is attended by 6,500 fans, with a standard deviation of 450 people.
This means that ![\mu = 6500, \sigma = 450](https://tex.z-dn.net/?f=%5Cmu%20%3D%206500%2C%20%5Csigma%20%3D%20450)
35 games:
This means that ![n = 35](https://tex.z-dn.net/?f=n%20%3D%2035)
Distribution of the sample mean:
By the Central Limit Theorem, we have
and the standard deviation is:
![\sigma_x = \frac{450}{\sqrt{35}} = 76](https://tex.z-dn.net/?f=%5Csigma_x%20%3D%20%5Cfrac%7B450%7D%7B%5Csqrt%7B35%7D%7D%20%3D%2076)