Samples of size n = 4000 are randomly selected from a

Question

population of homeowners in Florida. The square footage of the home is recorded and the mean is found for each sample. What is the distribution of the sample mean?
(1 point)
distribution skewed to the left
normal distribution
distribution skewed to the right
uniform distribution

Answer 1

According to the Central Limit Theorem, when sampling from a population with a sufficiently large sample size (typically n ≥ 30 is considered enough), the distribution of the sample means will be approximately normally distributed, regardless of the shape of the population distribution, as long as the samples are independent and randomly selected.

Given that the sample size \( n = 4000 \) is quite large, the distribution of the sample mean of the square footage of homes in Florida will be approximately a normal distribution.

So, the answer is normal distribution.