6
AssignmentMultiple Choice

Sampling Distribution of the Sample Mean

Question 6 • NC-Math 4

The number of children per household in the US is strongly skewed to the right. A person studying demographics selects an SRS of size n = 40 from the population of all households in the US and calculates the sample mean number of children per household. What is the shape of the distribution of the sample mean for all possible simple random samples of size 40 from this population?

Answer
A
skewed to the right
B
skewed to the left
C
approximately uniform
D
approximately Normal

Explanation

The population distribution is strongly skewed right, but the sample mean averages observations from 40 households. By the Central Limit Theorem, for a sufficiently large sample size, the distribution of sample means is approximately Normal, even when the population is skewed. Thus, the distribution is approximately Normal.

AI-written and checked against the verified answer.

Previous
Next