Housing has become more affordable over the past couple of decades, thanks to lo

Question

Housing has become more affordable over the past couple of decades, thanks to low inflation and low interest rates. Soon-to-be buyers participating in the National Association of Home Builders' 2001 buyer-preference survey indicated that they typically spent between six months and a year to buy a home. Suppose that the distribution of the time that it takes to buy a home can be approximated by a normal distribution with a mean of nine months and a standard deviation of three months. a. What is the probability that a home buyer selected at random spends less than a year to buy a home? b. At least what amount of time would 60% of the home buyers be expected to spend looking for a home to buy?

Explanation / Answer

Required probability is the probability that z = +1 and we have to find the cumulative probability for that.

Z = (12-9)/3 = 1

Using normal tables,Probability = 0.841345

Using,normal distribution tables, z value for cumulative probability of 0.60 is 0.253347

Hence, 60% people would spend atleas [9 + 0.253 *3) months to buy the home = 9.76 months

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