Question

The average sale price of new one-family houses in the United States for 2003 was $246,300. Using Chebyshev's theorem, find the range of values in which at least 75% of the sale prices will lie if the standard deviation is $48,500. Hint: You should memorize that when k is 2, it is 75% and when k is 3 it is 88.89%. Please answer with whole numbers: ex. 55,232 to 65,450 with commas

Answer 1

75% of the sales prices lie between $149,300 and $343,300 Chebyshev's theorem is weaker than the amount of numbers that lie within 2 standard deviations of the mean and requires that only 75% of the numbers in the distribution lie within 2 standard deviations. Since the standard deviation given is 48500, 2 standard deviations will be 2 * 48500 = 97000. Now the lower limit will be 246300 - 97000 and the upper limit will be 246300 + 97000. So Lower limit = 246300 - 97000 = 149300 Upper limit = 246300 + 97000 = 343300 So 75% of the sales prices will be between $149,300 and $343,300