Answer:
The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to 0.248.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Of the 500 people sampled, 124 said that they would be interested in purchasing season tickets to a Six Flags in Ames.
This means that
The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to
By the Central Limit Theorem, it is equal to the sample proportion of 0.248.