Question

Assume the loan balance (unpaid) of a defaulting loan from PSCU follows a nom distribution with mean $8,050 and variance 25,000,000 dollars2. a normal ,U-80S0 στ2S ,000,000 a) PSCU defines a catastrophic default as a default with a loan bala 1%. Wh at is the least amoupt which is considered to be catastrophic? 10 points O b) Find the probability that a loan default will be at least $6000. 5 points

Answer 1

Solution:-

Mean = 8050, S.D = 5000

a) The least amount which is considered to be catastrophic is 19685.

p-value for the highest 1% = 1 - 0.01 = 0.99

z-score for the p-value = +2.327

By applying normal distribution:-

$z=\frac{x-\mu }{\sigma }$

x = 19685

b) The probability that a loan default will be atleast $6000 is 0.659

x = 6000

By applying normal distribution:-

$z=\frac{x-\mu }{\sigma }$

z = -0.41

P(z > - 0.41) = 0.659