Answer:
The point estimate for the population standard deviation of the length of the curtains is 8.58in.
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, we have that:
[tex]s = 0.8, n = 115[/tex]
The point estimate for the population standard deviation of the length of the curtains is [tex]\sigma[/tex]. So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]\sigma = s\sqrt{n}[/tex]
[tex]\sigma = 0.8\sqrt{115}[/tex]
[tex]\sigma = 8.58[/tex]
The point estimate for the population standard deviation of the length of the curtains is 8.58in.
