The default rate on US government-guaranteed student loans to students attending

Question

The default rate on US government-guaranteed student loans to students attending a public four-year institution is 10 percent. We assume Statistical Independence.

a). If 1,000 student loans are made, what is expected number of those loans that end up in default? Round your answer to 1 decimal place

b). and the standard deviation? Round your answer to 1 decimal place

c). If 1,000 student loans are made, what is the probability of fewer than 109 defaults? Select best, closest, answer from the choices below.

0.0001 0.01 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 0.9990

Explanation / Answer

We are considering giving loan as success. So here we have a binomial distribution with n=1000 and p=0.1

a.Now expected number of those loans that end up in default=np=1000*0.1=100.0

b.standard deviation=sqrt(npq)=sqrt(1000*0.1*0.9)=9.5

c.If we take confidence interval then we need to find the value of a for which,

np+za*n*(sqrt(pq/n))=109.

this implies za=0.94

From normal table using the value of 2*.94=1.88 we find the required probability close to 0.99.

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