Respuesta :
Answer:
The probability that exactly one of these mortgages is delinquent is 0.357.
Step-by-step explanation:
We are given that 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.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 8 mortgages
r = number of success = exactly one
p = probability of success which in our question is % of U.S.
mortgages those were delinquent in 2011, i.e; 8%
LET X = Number of U.S. mortgages those were delinquent in 2011
So, it means X ~ [tex]Binom(n=8, p=0.08)[/tex]
Now, Probability that exactly one of these mortgages is delinquent is given by = P(X = 1)
P(X = 1) = [tex]\binom{8}{1}\times 0.08^{1} \times (1-0.08)^{8-1}[/tex]
= [tex]8 \times 0.08 \times 0.92^{7}[/tex]
= 0.357
Hence, the probability that exactly one of these mortgages is delinquent is 0.357.
