According to the Mortgage Bankers Association,8% of U.S.mortgages were delinquent in 2011.A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure.A random sample of eight mortgages was selected.What is the probability that exactly one of these mortgages is delinquent?
A) 0.1296
B) 0.3570
C) 0.4926
D) 0.6157

Question

Quizplus · Accepted Answer

This problem follows a binomial distribution with n=8 (number of mortgages) and p=0.08 (probability of a delinquent mortgage). We want to find the probability of exactly one delinquent mortgage, which is represented by the formula P(X=1) = (n choose x) * p^x * (1-p)^(n-x), where (n choose x) is the binomial coefficient. Plugging in the values, we get P(X=1) = (8 choose 1) * 0.08^1 * 0.92^7 = 0.3570, which is option B.