Answer:
n = 100 scores from a population with σ = 20
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, of [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
n = 5 scores from a population with σ = 20
[tex]s = \frac{20}{\sqrt{5}} = 8.94[/tex]
n = 5 scores from a population with σ = 80
[tex]s = \frac{80}{\sqrt{5}} = 35.78[/tex]
n = 100 scores from a population with σ = 20
[tex]s = \frac{20}{\sqrt{100}} = 2[/tex].
This one is the correct answer.
n = 100 scores from a population with σ = 40
[tex]s = \frac{40}{\sqrt{100}} = 4[/tex].
