The foreclosure crisis has been particularly devastating in housing markets in much of the south and west United States, but even when analysis is restricted to relatively strong housing markets the numbers are staggering. For example, in 2017 an average of three residential properties were auctioned off each weekday in the city of Boston, up from an average of one per week in 2011. What is the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2017 in Boston?
A) 0.1680
B) 0.1954
C) 0.2240
D) 0.8153

Question

Quizplus · Accepted Answer

This problem involves the Poisson distribution, which is used to model the number of rare events (in this case, foreclosure auctions) that occur in a fixed unit of time or space. The Poisson distribution has a single parameter, lambda, which represents the average number of events that occur in the unit of time or space.

In this problem, we are told that on average three residential properties were auctioned off each weekday in 2017 in Boston. Therefore, lambda = 3.

To find the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2017 in Boston, we can use the Poisson probability mass function:

P(X = 4) = (e^-3)*(3^4)/4! = 0.1680

Therefore, the answer is choice A, 0.1680.

The Foreclosure Crisis Has Been Particularly Devastating in Housing Markets