Suppose 35% of homes in a Miami,Florida,neighborhood are under water (in other words,the amount due on the mortgage is larger than the value of the home).There are 160 homes in the neighborhood and 30 of those homes are owned by your friends.What is the probability that less than 30% of your friend's homes are under water?
A)0.2611
B)0.2843
C)0.6400
D)0.7389

Question

Quizplus · Accepted Answer

We can use the binomial distribution formula to solve this problem. Let X be the number of homes under water out of the 30 homes owned by your friends. Then, X ~ B(30, 0.35), since the probability of a home being under water is 0.35. We want to find P(X < 0.3*30) = P(X < 9), since we are looking for the probability that less than 30% of your friends' homes are under water.

Using a binomial distribution table or calculator, we get P(X < 9) = 0.2611. Therefore, the best choice is (A).

Suppose 35% of Homes in a Miami,Florida,neighborhood Are Under Water