Question

1. For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed.

1. What is the probability that the debt for a borrower with good credit is more than $18,000?
2. What is the probability that the debt for a borrower with good credit is less than $10,000?
3. What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000?
4. What is the probability that the debt for a borrower with good credit is no more than $14,000?

Answer 1

Let X be the debt for a borrower with good credits. Then from the question, it is known that X follows Normal distribution with mean debt $15015 and standard deviation $3540. Then define a random variable Z=(X-mean)/Standard deviation, Z follows normal distribution with mean 0 and standard deviation 1. In other words, Z follows standard Normal distribution.

Now the probabilities can be calculated using standard normal cumulative table as follows

(a) The required probability is

P(X>18000)=

where value of is obtained using standard normal cumulative table.

Similarly

(b) The required probability is

P(X<10000)=

(c) The required probability is

P(12000<X<18000)=

(d) The required probability is

P(X≤14000)=