Using the Central Limit Theorem, it is found that the standard deviation for the sampling distribution of sample means is given by:
[tex]s = \frac{\sigma}{\sqrt{51}}[/tex].
The Central Limit Theorem states that, the sampling distribution of sample means of size n, from a population with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], has mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question, 51 samples, hence, [tex]n = 51[/tex]
Hence, applying the Central Limit Theorem, the standard deviation for the sampling distribution of sample means is given by:
[tex]s = \frac{\sigma}{\sqrt{51}}[/tex].
A similar problem, which also involves the Central Limit Theorem, is given at https://brainly.com/question/24663213
