Question

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 fewer than 30% of your friends’ homes are under water?

Answer 1

We are given proportion of homes under water P = 0.35 so q = 1-0.35 = 0.65

and there are N =160 homes in the neighborhood and n = 30 of those homes are owned by your friends

As n/N = 30/ 160 = 0.1875 > 0.05 we have to use continuity correction factor while finding the standard deviation of

follow approximately normal distribution with mean( µ) = P = 0.35 and

Standard deviation ( σ) = = = 0.0787

We are asked to find P( < 0.30)

=

=P( z < -0.64)

=0.2611