Question: A family is considering a move from a midwestern city to a city in California. The 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.
a. What percentage of houses in the family's current city cost less than theirs?
b. If the family buys a $200,000 house in the new city, what percentage of houses there will cost less than theirs?
c. 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?