1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sliva [168]
3 years ago
12

Suppose the selling price of homes is skewed right with a mean of 350,000 and a standard deviation of 160000 If we record the se

lling price of 40 randomly selected US homes what will be the shape of the distribution of sample means what will be the mean of this distribution what will be the standard deviation of this distribution
Mathematics
2 answers:
lys-0071 [83]3 years ago
5 0

Answer:

The distribution will be approximately normal, with mean 350,000 and standard deviation 25,298.

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:

Suppose the selling price of homes is skewed right with a mean of 350,000 and a standard deviation of 160000

Sample of 40

Shape approximately normal

Mean 350000

Standard deviation s = \frac{160000}{\sqrt{40}} = 25298

The distribution will be approximately normal, with mean 350,000 and standard deviation 25,298.

nika2105 [10]3 years ago
5 0

Answer:

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

The mean would be:

\mu_{\bar X} =350000

And the standard deviation would be:

\sigma_{\bar X} =\frac{160000}{\sqrt{40}}= 25298.221

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the selling price of a population, and for this case we know the following info

Where \mu=350000 and \sigma=160000

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

The mean would be:

\mu_{\bar X} =350000

And the standard deviation would be:

\sigma_{\bar X} =\frac{160000}{\sqrt{40}}= 25298.221

You might be interested in
How do I solve (7-6i)(-8+3i)?
Alekssandra [29.7K]
I = {2.666666667, 1.166666667
6 0
3 years ago
Read 2 more answers
Finding area of shaded sectors.
tekilochka [14]

Answer:

69.81 sq. m. (rounded to 2 decimal places)

Step-by-step explanation:

The sector of a circle is "part" or "portion" of a circle. The formula for the area of a sector is:

A=\frac{\theta}{360}*\pi r^2

Where

\theta  is the central angle

r is the radius

Given the figure, the arc is given as 80 degrees, but not the central angle of the shaded sector. But from geometry we know that the central angle and the intercepted arc have the same measure. So we can say:

\theta = 80

Also, the radius of the circle shown is 10 meters, so

r = 10

Now, we substitute in formula and find our answer:

A=\frac{\theta}{360}*\pi r^2\\A=\frac{80}{360}*\pi (10)^2\\A=\frac{2}{9}*100\pi\\A=\frac{200\pi}{9}\\A=69.81

Thus,

The area of the shaded sector is 69.81 sq. meters.

5 0
3 years ago
What is the formula for a confidence interval?
ikadub [295]

Answer:

a) The formula is given by mean \pm the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

b) \bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

Part a

The formula is given by mean \pm the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

Part b

The confidence interval for the mean is given by the following formula:  

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

5 0
3 years ago
Ben, Bob and Bill are triplets. They were born 5 years before their sister, Stephanie. This year the product of their four ages
maria [59]

Let the triplets' age be x, the sister's age is then x-5. 
product of their age as given 
xÂł.(x-5)=75749+x+x+x+x-5
 x^4 - 5xÂł= 4x +75744
 x^4 - 5xÂł -4x -75744=0
 resolving the equation,
 we get 
 x = 18 
 therefore, Age of ben,bob and bill is 18
 so , age of stephanie is x-5 = 18-5 = 13
 stephanie is 13 years old.

3 0
3 years ago
Please I need help ASAP
ira [324]

you just answer ths but here this might help

plz mark as brainliest

7 0
3 years ago
Other questions:
  • Can someone please help me on this one!!!!
    10·1 answer
  • Chelsea needs to take a taxi home and lives 7 miles away. The taxi company charges $4 plus $1.50 per mile. How much will she pay
    11·1 answer
  • Mr. Abernathy purchased a selection of wrenches for his shop. The total cost was $78. He bought the same number of $1.50 and $2.
    10·1 answer
  • 1.147 as a percentage​
    11·2 answers
  • A wheel rolling at a constant speed has a radius of 15 inches and takes 30
    15·1 answer
  • Kermit ran 100 meters in 12.35 seconds. Gonzo ran 100 meters in 11.915 seconds. How much faster did Gonzo run than Kermit? secon
    9·1 answer
  • Find the interquartile range (IQR) for the following data set:
    11·1 answer
  • Neha used 4 bananas and 5 oranges in her fruit salad. Daniel used 7 bananas and 9 oranges. Did Neha and Daniel use the same rati
    10·1 answer
  • You are wrapping a gift box that is 16 inches long, 7 inches wide, and 9 inches tall. Find the amount of wrapping paper you need
    9·1 answer
  • Here all the other ones .
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!