Question

A population has Mu = 60 with standard deviation = 5. What is the expected value of a distribution of sample means for samples of size n = 4 selected from this population? a) 5 b) 60 c) 15 d) not enough info

Answer 1

The expected value of the distribution of sample means for samples of size 4 from a population with a mean of 60 is 60.

Step-by-step explanation:

The expected value of a distribution of sample means, also known as the sampling distribution of the sample mean, for samples of size n = 4 selected from a population with a mean (μ) of 60 and a standard deviation (σ) of 5 is equal to the population mean. This is derived from the Central Limit Theorem, which states that the distribution of sample means will be normally distributed around the population mean, regardless of the sample size, as long as the sample size is sufficiently large (usually n ≥ 30 is sufficient, but smaller samples also often work with normally distributed populations). In this case, the correct answer is b) 60.