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Fiesta28
2 months ago
8

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these h

omes 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
Mathematics
1 answer:
tester [12.3K]2 months ago
4 0

Answer:

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

Step-by-step explanation:

The Central Limit Theorem asserts that for a random variable X that follows a normal distribution with a mean of \mu and a standard deviation of \sigma, the sampling distribution of sample means, when drawn with size n, can be estimated as a normal distribution with a mean of \mu and a standard deviation of s = \frac{\sigma}{\sqrt{n}}.

Even if the variable is skewed, as long as n is no less than 30, the Central Limit Theorem still holds.

Population:

Right skewed

Mean $206,274

Standard deviation $37,881.

Sample:

<pbased on="" the="" central="" limit="" theorem="" it="" can="" be="" approximated="" to="" normal.="">

Mean $206,274

Standard deviation s = \frac{37881}{\sqrt{100}} = 3788.1

So the correct answer is:

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

</pbased>
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