Question

The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. the manager at one of the stores randomly selects 30 pairs of pants. what is the shape of the distribution of the sample mean for all possible random samples of size 30 from this population? skewed left skewed right approximately normal approximately uniform

Answer 1

The distribution of the sample mean for all possible random samples of size 30 from a population with a left-skewed distribution will be approximately normal, due to the central limit theorem.

Step-by-step explanation:

The question refers to the central limit theorem, which states that when you have a sufficiently large sample size (typically n ≥ 30), the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. Since the manager selects 30 pairs of pants, which is the threshold for the central limit theorem, the distribution of the sample mean for all possible random samples of that size from the population will be approximately normal. This is a key concept in statistics that enables us to make inferences about population parameters based on sample statistics.