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Normal Distribution: First Mortgage

The average conventional first mortgage for new single-family homes was $294,000. Assuming a normal distribution and a standard deviation of o = $30,000, what proportion of the mortgages were:
a. more than $294,000?
b. between $234,000 and $354,000?
c. between $264,000 and $342,000?
d. more than $204,000?

Solution Preview

Suppose the mortgage is X, it has means m = $294,000 and standard deviation o = $30,000.
Let Y = (X - m)/o = (X - 294000)/30000, then X = 30000Y + ...

Solution Summary

This solution contains explanations as well as calculations with regards to calculating proportions and probability in the context of first mortgages.