Answer:
By the Central Limit Theorem, the distribution of the sample mean will be normally distributed with mean [tex]\mu = 71[/tex] and standard deviation [tex]s = \frac{3.56}{\sqrt{40}} = 0.5629[/tex]
Step-by-step explanation:
We use the Central Limit Theorem to solve this problem.
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size, of at least 30, can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that
[tex]\mu = 71, \sigma = 3.56[/tex]
What is the distribution of the sample mean?
By the Central Limit Theorem, the distribution of the sample mean will be normally distributed with mean [tex]\mu = 71[/tex] and standard deviation [tex]s = \frac{3.56}{\sqrt{40}} = 0.5629[/tex]
