Question Tag: Loan Defaults

The distribution of the total loan amounts defaulted by customers of a bank annually is approximated by a normal distribution. The average default amount is GH¢1.50 million, and the standard deviation is GH¢0.50 million.

Required:
a) Determine the probability that the total loan amount defaulted exceeds GH¢1.50 million. (3 marks)
b) Determine the probability that the total loan amount defaulted is between GH¢0.86 million and GH¢0.90 million. (4 marks)
c) Determine the probability that the total amount defaulted is at most GH¢2 million. (4 marks)
d) Determine the amount to be allowed per annum for loan defaults if 1% of actual defaults exceed this amount. (3 marks)
e) Determine the lower quartile of the distribution of total loan amounts defaulted. (3 marks)
f) Determine the upper quartile of the distribution of total loan amounts defaulted. (3 marks)
(Total: 20 marks)