Answer:
A sample size of 400 was used in the study.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation(standard error) [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, we have that:
[tex]\sigma = 860, s = 43[/tex]
We have to find n.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]43 = \frac{860}{\sqrt{n}}[/tex]
[tex]43\sqrt{n} = 860[/tex]
[tex]\sqrt{n} = \frac{860}{43}[/tex]
[tex]\sqrt{n} = 20[/tex]
[tex](\sqrt{n})^{2} = 20^{2}[/tex]
[tex]n = 400[/tex]
A sample size of 400 was used in the study.
