1.City X is a popular coastal destination with a pleasant mild climate. The average price of detached houses in city X is $715,000, with a standard deviation of $369,000. On the other hand, city Y is land-locked in the northern heart of the continent, with a harsh continental climate. The average price of detached houses in city Y is $359,000, with a standard deviation of $228,000. The two markets for detached housing are normally distributed.

a)What is the z-score of a $1 million house on each of these distributions?

b)What percentage of houses cost $1 Million in city X? In city Y?

c)What percentage of houses on market X falls between $820,000 and $1,500,000?

d)What percentage of houses on market Y falls between $100,000 and $250,000?

Note: For each of the above questions, show calculations.