Question

A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of bar(x) is approximately normal because _____.

Answer 1

A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of bar(x) is approximately normal because _____

Answer: A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of bar(x) is approximately normal because of the central limit theorem.

Central Limit Theorem: The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30).