Question

Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is that housing prices follow an approximately normal model with mean $250,000 and standard deviation $6,706. (a) What proportion of housing prices in Athens are less than $239,000? (3 decimal places) (b) A realtor takes a random sample of 117 houses in Athens. Determine the probability the average selling price is greater than $251,000? (3 decimal places) (c) A realtor in Asheville, NC wants to estimate the mean housing price of houses in Asheville. The realtor believes the distribution of housing prices in Asheville is similar to those in Athens. If this realtor takes a random sample of 117 homes in Asheville, what is the standard error of the estimate? (3 decimal places) How many homes in Asheville should the realtor sample to be 95% confident the estimate is within $500 of the true mean price? Use the critical value to exactly 3 decimal places.

Answer 1

Von Oto Aws) Given data U=250,000 o=6706 a) P(xc 239000) = Plzc239000 - 250000 6706 =P(Z <=1064) 50.0505 =>0.051 b) For n=117, X=Mx =250000 Gz = 670 = 619.97 Pl x>251000) = P(Z >251000-250000 019-97 = I-P(Z<1.G13) 31-0.946628 -0.053372 20.053 112

c) For n=117, standard Error q = 0 =619.97 Now e=500, For 95%CI, Zx2=1-96 Sample size n= (22/2x02 n = 11-96X6706) soo n=691