Question

Assume the average selling price for houses in a certain county is ​\$321000 with a standard...

Assume the average selling price for houses in a certain county is ​\$321000 with a standard deviation of ​\$34000. ​

a) Determine the coefficient of variation. ​

b) Caculate the​ z-score for a house that sells for ​\$358000. ​

c) Using the Empirical​ Rule, determine the range of prices that includes 68​% of the homes around the mean.

​d) Using​ Chebychev's Theorem, determine the range of prices that includes at least 93​% of the homes around the mean.

Given,

mean = = \$321000

Standard deviation = = \$34000

a)

To determine the coefficient of variation

Here coefficient of variation = /

substitute values

= 34000/321000

= 0.1059

b)

To calculate the z score for a house that sells for \$358000

Z - score = (X - )/

= (358000 - 321000) / 34000

= 37000/34000

= 1.0882

c)

To determine the range of prices that includes 68% of home around mean

Now by utilizing empirical formula,

68% is within the 1 one standard deviation of mean

68% is within 321000 +/- 34000

= (321000 - 34000 . 321000 + 34000)

= (287000 , 355000)

d)

To determine the range of prices that includes 93% of homes around mean

proportion of data within the k standard deviation of mean is given as follows

= (1 - 1/k^2)

So (1 - 1/k^2) = 0.93

1/k^2 = 1 - 0.93

1/k^2 = 0.07

k^2 = 1/.07

k^2 = 14.2857

k = 3.7796

So at least 93% is in interval = mean +/- k*standard deviation

substitute values

= 321000 +/- 3.7796*34000

= 321000 +/- 128506.4

= (321000 - 128506.4 , 321000 + 128506.4)

= (192494 , 449507)