Question

a simple random sample is drawn from a normally distributed population. the value of which of the following will not be known for certain but can be inferred?
○ μ
○ x̄
○ s
○ n

Explanation:

• $\mu$ (population mean): When we take a sample from a population, the true population mean $\mu$ is generally unknown. We use sample statistics (like the sample mean $\bar{x}$) to make inferences (estimates) about $\mu$.
• $\bar{x}$ (sample mean): We can calculate the sample mean directly from the sample data we collect, so its value is known.
• $s$ (sample standard deviation): We can compute the sample standard deviation from the sample data, so its value is known.
• $n$ (sample size): We know how many observations we included in our sample, so $n$ is known.

So the value that is not known for certain but can be inferred is $\mu$.

Answer:

A. $\mu$