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

Solution :

Given that ,

mean = = $15015

standard deviation = = $3540

a.

P(x > $18000) = 1 - P(x < 18000)

= 1 - P[(x - ) / < (18000 - 15015) / 3540)

= 1 - P(z < 0.84)

= 1 - 0.7995

= 0.2005

Probability = 0.2005

b.

P(x < $10000) = P[(x - ) / < (10000 - 15015) / 3540]

= P(z < -1.42)

= 0.0778

Probability = 0.0778

c.

P($12000 < x < $18000) = P[(12000 - 15015)/ 3540) < (x - ) /  < (18000 - 15015) / 3540) ]

= P(-0.85 < z < 0.84)

= P(z < 0.84) - P(z < -0.85)

= 0.7995 - 0.1977

= 0.6018

Probability = 0.6018

d.

P(x $14000)

= P[(x - ) / (14000 - 15015) / 3540]

= P(z -0.29)

= 0.3859

Probability = 0.3859