SOLUTION: The default rate on government-guaranteed student loans at a certaing public 4-year institution is 7% (a) If 1,000 student loans are made, what is the probability of fewer than 50

Question 128858This question is from textbook applied staistics in business and economics
: The default rate on government-guaranteed student loans at a certaing public 4-year institution is 7% (a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults? (b) More than 100? Show your work carefully.
This question is from textbook applied staistics in business and economics

Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!
The default rate on government-guaranteed student loans at a certain public 4-year institution is 7%
(a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults?
It's a binomial problem but the large n requires using a normal approximation.
mean = np = 1000*0.07 = 70
std = sqrt(npq) = sqrt(70*0.93) = 8.0685
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z(50) = (50-70)/[8.0685] = -2.4788
P(# of defaults < 50) = P(z<-2.4788) = 0.0066
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(b) More than 100?
z(100) = (100-70)/8.0685 = 3.7182
P(defaults > 100) = P(z>3.7182) = 0.00010035..
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Cheers,
Stan H.