Question

The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include. The average game is attended by 6,500 fans, with a standard deviation of 450 people. Suppose a random sample of 35 games is selected to help the owners decide the number of seats to include. Identify each of the following and be sure to round to the nearest whole number:

Provide your answer below:
μ =------------
μx=-----------
σx=-----------
σ=------------
n=------------

Answer 1

μ = 6500

μx= 6500

σx= 76

σ= 450

n= 35

Explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

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`

35 games:

This means that
`n = 35`

Distribution of the sample mean:

By the Central Limit Theorem, we have
`\mu_x = \mu = 6500` and the standard deviation is:

`\sigma_x = (450)/(√(35)) = 76`