Respuesta :
Answer:
(A) Approximately normal with mean $206,274 and standard deviation $3,788
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.
Population:
Right skewed
Mean $206,274
Standard deviation $37,881.
Sample:
By the Central Limit Theorem, approximately normal.
Mean $206,274
Standard deviation [tex]s = \frac{37881}{\sqrt{100}} = 3788.1[/tex]
So the correct answer is:
(A) Approximately normal with mean $206,274 and standard deviation $3,788
Approximately normal with mean is $206,274 and standard deviation is $3,788 and this can be determined by applying the central limit theorem.
Given :
- There were 5,317 previously owned homes sold in a western city in the year 2000.
- The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881.
- Simple random samples of size 100.
According to the central limit theorem the approximately normal mean is $206274.
Now, to determine the approximately normal standard deviation, use the below formula:
[tex]s =\dfrac{\sigma }{\sqrt{n} }[/tex] ---- (1)
where 's' is the approximately normal standard deviation, 'n' is the sample size, and [tex]\sigma[/tex] is the standard deviation.
Now, put the known values in the equation (1).
[tex]s = \dfrac{37881}{\sqrt{100} }[/tex]
s = 3788.1
[tex]\rm s \approx 3788[/tex]
So, the correct option is A).
For more information, refer to the link given below:
https://brainly.com/question/18403552
