Answer:
[tex]\mu_{x} = 64, \sigma_{x} = 12.83[/tex]
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 of at least 30 can be approximated to a normal distribution with mean [tex]\mu_{x} = \mu[/tex] and standard deviation [tex]\sigma_{x} = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]\mu = 64, \sigma = 77, n = 36[/tex]
So
[tex]\mu_{x} = 64, \sigma_{x} = \frac{77}{\sqrt{36}} = 12.83[/tex]
