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. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?
(A) Approximately normal with mean $206,274 and standard deviation $3,788
(B) Approximately normal with mean $206,274 and standard deviation $37,881
(C) Approximately normal with mean $206,274 and standard deviation $520
(D) Strongly right-skewed with mean $206,274 and standard deviation $3,788
(E) Strongly right-skewed with mean $206,274 and standard deviation $37,881

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 :

According to the central limit theorem the approximately normal mean is $206274.

Now, to determine the approximately normal standard deviation, use the below formula:

  ---- (1)

where 's' is the approximately normal standard deviation, 'n' is the sample size, and is the standard deviation.

Now, put the known values in the equation (1).

s = 3788.1

So, the correct option is A).

For more information, refer to the link given below:

link

(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 and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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

So the correct answer is:

(A) Approximately normal with mean $206,274 and standard deviation $3,788

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step-by-step explanation: