Respuesta :
Answer:
The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.
The sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.
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 [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem
The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.
If it is:
[tex]\mu = 63, \sigma = 18, n = 10, s = \frac{18}{\sqrt{10}} = 5.69[/tex]
The sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.
