Question

Determine

Answer 1

Answer:

$\mu_{x} = 64, \sigma_{x} = 12.83$

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu_{x} = \mu$ and standard deviation $\sigma_{x} = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 64, \sigma = 77, n = 36$

So

$\mu_{x} = 64, \sigma_{x} = \frac{77}{\sqrt{36}} = 12.83$