Question

According to a recent​ study, 23% of U.S. mortgages were delinquent last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of twelve mortgages was selected. What is the probability that greater than 5 of these mortgages are delinquent?

Answer 1

P ( X > 5) = 0.0374

Explanation:

Given:

n = 12

p = 0.23

Using Binomial distribution formula,

X ~ Binomial ( n = 12, p = 0.23)

`=(n!)/((n-x)! x!). p^(x) q^(n-x)`

Substitute for n = 12, p = 0.23, q = 1-0.23 for x = 6,7,8,9,10,11 and 12

P (X > 5) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) + P(X=11) + P(X=12)

P ( X > 5 ) = 0.0285 + 0.007299 + 0.00136 + 0.000181 + 0.0000162 + 1E-6 + 1E-6

P ( X > 5) = 0.0374