Question

assume the average selling price for houses in a certain county is ​$295 comma 000 with a standard deviation of ​$56 comma 000. ​a) Determine the coefficient of variation. ​b) Caculate the​ z-score for a house that sells for ​$283 comma 000. ​c) Using the Empirical​ Rule, determine the range of prices that includes 95​% of the homes around the mean. ​d) Using​ Chebychev's Theorem, determine the range of prices that includes at least 90​% of the homes around the mean. ​a) Determine the coefficient of variation. CVequals 18.99​% ​(Round to one decimal place as​ needed.) ​b) Calculate the​ z-score for a house that sells for ​$283 comma 000. zequals negative 0.21  ​(Round to two decimal places as​ needed.) ​c) Using the Empirical​ Rule, determine the range of prices that includes 95​% of the homes around the mean. upper bound x equals ​$ nothing lower bound x equals ​$ nothing ​(Round to the nearest dollar as​ needed.) ​d) Using​ Chebychev's Theorem, determine the range of prices that includes at least 90​% of the homes around the mean. upper bound x equals ​$ nothing lower bound x equals ​$ nothing ​(Round to the nearest dollar as​ needed.)

Answer 1

Answer:

a) 18.98%

b) -0.2142

c) (183000,407000)

d) (127000,463000)

Step-by-step explanation:

We are given the following in the question:

Mean, μ = ​$295,000

Standard Deviation, σ = $56,000

a) Coefficient of variation

$COV =\dfrac{\sigma}{\mu} = \dfrac{56000}{295000}\\\\=0.1898\\=18.98\%$

b)  z-score

x = $283,000

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Putting the value, we get,

$z_{score} = \displaystyle\frac{283000-295000}{56000} = -0.2142$

c) 95% interval

Empirical Rule:

• According to this rule almost all the data lies within three standard deviation of mean for a normal distribution.
• About 68% of data lies within one standard deviation of mean.
• About 95% of data lies within two standard deviation of mean.

$\mu \pm 2(\sigma)\\=295000 \pm 2(56000)\\=(183000,407000)$

Thus, the price of 95​% of the homes lies between $183,000 and $407,000.

d) 90% interval

Chebyshev's Rule:

• For a non normal data atleast $1-\dfrac{1}{k^2}$  percent of data lies within k standard deviation of mean.
• For k = 3

$1 - \dfrac{1}{(3)^2} = 88.89\% \approx 90\%$

Thus, 90% of prices will lies within three standard deviation of mean.

$\mu \pm 3(\sigma)\\=295000 \pm 3(56000)\\=(127000,463000)$

According to Chebyshev's Theorem 90% of prices will lie between $127,000 and $463,000.