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 and do NOT enter the units given that Connect has trouble grading the units.

Expected number of loans that end up in default is:_____

b). and the standard deviation? Round your answer to 1 decimal place and do NOT enter the units given that Connect has trouble grading the units.

Standard deviation for the number of loans that end up in default is:____

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

a)

Here, n = 1000, p = 0.10, so

u = mean = np =    100 [ANSWER]

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b)
  
s = standard deviation = sqrt(np(1-p)) =    9.486832981 [ANSWER]

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c)

We first get the z score for the critical value:          
          
x = critical value =    108.5      
u = mean = np =    100      
          
s = standard deviation = sqrt(np(1-p)) =    9.486832981      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    0.89597867      
          
Thus, the left tailed area is          
          
P(z <   0.89597867   ) =    0.814867922 = 0.8 [ANSWER]

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