Mathematics, 03.06.2020 03:00 animerocks07

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

Answers: 3

Show answers

Answers

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:

$s =\dfrac{\sigma }{\sqrt{n} }$ ---- (1)

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

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

$s = \dfrac{37881}{\sqrt{100} }$

s = 3788.1

$\rm s \approx 3788$

So, the correct option is A).

For more information, refer to the link given below:

link

Answer from: hayesgenniferozslxr

(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 $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

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 $s = \frac{37881}{\sqrt{100}} = 3788.1$

So the correct answer is:

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

Answer from: Quest

welll its a very hard question but ill

step-by-step explanation:

first you take the 6 dollars and add 10 to it then add the 50 to that then multiply by 8 with xy and your answer will be

hope this

Answer from: Quest

Ibelieve it's a. 2.2 - x = -10.85 (plz tell me if it's right : ) )

Another question on Mathematics

Mathematics, 21.06.2019 18:30

The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Marina baked cookies. she gave 3/4 of the cookies to the scout bake sale. she shared the remaining 6 cookies with her friends. how many cookies did marina bake?

Answers: 3

Answer

Mathematics, 21.06.2019 20:00

Which type of graph would allow us to quickly see how many students between 100 and 200 students were treated?

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

Evaluate 5 + 6 · 2 – 8 ÷ 4 + 7 using the correct order of operations. a. 22 b. 11 c. 27 d. 5

Answers: 1

Answer

You know the right answer?

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