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 2011 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 2005.What is the probability that exactly four foreclosure auctions occurred on a randomly selected weekday of 2011 in Boston?
A) 0.1680
B) 0.1954
C) 0.2240
D) 0.8153

Question

Quizplus · Accepted Answer

The problem can be modeled using a Poisson distribution, where the average rate (λ) is 3 foreclosures per weekday. The probability of exactly k events (k=4) is given by the formula P(X=k) = (e^(-λ) * λ^k) / k!. Plugging in the values, we get P(X=4) = (e^(-3) * 3^4) / 4! = 0.1680.

The Foreclosure Crisis Has Been Particularly Devastating in Housing Markets