Question

According to the Mortgage Bankers Association, 11% 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 eight mortgages was selected. What is standard deviation of this distribution?

Answer 1

Answer:

The standard deviation of this distribution is 0.8850.

Step-by-step explanation:

For each U.S. mortgage in the sample, there are only two possible outcomes. Either it is delinquent, or it is not. The probabilities of each mortgages being delinquent are independent from one another. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

11% of U.S. mortgages were delinquent last year.

This means that $p = 0.11$

A random sample of eight mortgages was selected. What is standard deviation of this distribution?

This is $\sqrt{V(X)}$ when $n = 8$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8*0.11*0.89} = 0.8850$

The standard deviation of this distribution is 0.8850.