Case Study: A family is considering a move form a mid-western city to a city in

Question

Case Study: A family is considering a move form a mid-western city to a city in California. The 10 distribution of housing costs where the family currently lives is normal, with mean $105,000 and standard deviation $18,200. The distribution of housing costs in the California city is normal with mean $235,000 and standard deviation $30,400. The family's current house is valued at $110,000 .Q1: What percentage of houses in the family's current city cost less than theirs? Q2 What price house will the family need to buy to be in the same percentile (of housing costs) in the new city as they are in the current city?

Explanation / Answer

1)
mean = 105000 , s = 18200
P(X < 110000)
z = ( x - mean) / s
= ( 110000 - 105000) / 18200
= 0.2747
P(X < 110000) = p(z < 0.2747) = 0.6082
Required perecentage = 60.82%

2)
to have the cost of new house within the same percentile as of current , we use the above calculated z value = 0.2747

mean = 235000 , s = 30400
z = ( x - mean) / s
0.2747 = (x - 235000)/ 30400
x = 31851.648
Hence, the new price should be $31851.648

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