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 10 foreclosure auctions occurred during a randomly selected five-day week in 2017 in Boston?
A) 0.0008
B) 0.0486
C) 0.1185
D) 0.9514

Question

Quizplus · Accepted Answer

We can use the Poisson distribution to solve this problem, since the number of foreclosure auctions per day follows a Poisson distribution with a mean of 3.

Let X be the number of foreclosure auctions during a five-day week in Boston. Then X follows a Poisson distribution with parameter λ = 3 * 5 = 15 (since the mean number of auctions over 5 days is just 3 * the number of days).

Using the Poisson probability formula, we find:

P(X = 10) = (e^(-15) * 15^10) / 10! ≈ 0.0486

Therefore, the probability of exactly 10 foreclosure auctions occurring during a randomly selected five-day week in 2017 in Boston is 0.0486 or approximately 4.86%.

The best choice is B because it correctly uses the Poisson distribution to calculate the probability.

The Foreclosure Crisis Has Been Particularly Devastating in Housing Markets