Exhibit 5-14.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. Refer to Exhibit 5-14.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 probability of exactly four foreclosure auctions occurring on a randomly selected weekday of 2011 in Boston is 0.1680. This is because the average number of foreclosure auctions per weekday in Boston in 2011 was three, and the Poisson distribution can be used to model the number of events that occur in a fixed interval of time or space if these events occur with a known average rate. The Poisson distribution is given by the formula P(X = k) = (e^-λ * λ^k) / k!, where λ is the average number of events per interval and k is the number of events that occur in the interval. In this case, λ = 3 and k = 4, so P(X = 4) = (e^-3 * 3^4) / 4! = 0.1680.