Answer:
μ= 65 inches; σ= 0.625 inch
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed(bell-shaped) 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, we have that:
[tex]\mu = 65, \sigma = 2.5[/tex]
By the central limit theorem, the sample of 16 will have:
[tex]\mu = 65, \sigma = \frac{2.5}{\sqrt{16}} = 0.625[/tex]
So the correct answer is:
μ= 65 inches; σ= 0.625 inch
