3.3.26 Question Help Assume the average selling price for houses in a certain co

Question

3.3.26 Question Help Assume the average selling price for houses in a certain county is $354,000 with a standard deviation of $32,000. a) Determine the coefficient of variation. b) Caculate the z-score for a house that sells for $382,000. 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 84% of the homes around the a) Determine the coefficient of variation. CV-1% (Round to one decimal place as needed.) Enter your answer in the answer box and then click Check Answer. parts remaining Clear All Check Answer

Explanation / Answer

a) CV = SD/Average = 32000/354000 = 9.0%

b) z - score for $382000 = (382000 - 354000)/32000 = 0.88

c) By empirical rule, 95% of data lies between two standard deviation from the mean. Hence,

Range of prices = (354000 - 2*32000) to (354000 + 2*32000) i.e. 290000 to 418000

d) By Chebyshev's theorem, atleast 84% of the data lies between 2.5 standard deviation from the mean. Hence,

Range of prices = (354000 - 2.5*32000) to (354000 + 2.5*32000) i.e. 274000 to 434000

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