during periods of economic recession experience shows that 1

during periods of economic recession, experience shows that 10% of the people with loans outstanding at a certain commercial bank will become delinquent in their loan repayment schedule. To examine this issue and the characteristics of borrowers from her bank, the bank president randomly selects n=100 account files at a time in which the economic climate of the community is very uncertain . Find the following probabilities: Ten or more of the borrowers are delinquent in their loan repayment schedule.

No more than 5 are delinquent.

Please give the full answer.

Solution

during periods of economic recession, experience shows that 10% of the people with loans outstanding at a certain commercial bank will become delinquent in their loan repayment schedule. To examine this issue and the characteristics of borrowers from her bank, the bank president randomly selects n=100 account files at a time in which the economic climate of the community is very uncertain . Find the following probabilities:

Normal approximation to binomial distribution used.

P=0.10

N=100

Expectation = np = 10

Variance = np(1 - p) = 9

Standard deviation = 3

Ten or more of the borrowers are delinquent in their loan repayment schedule.

P(x >= 10 ) = P( x >9.5) = p( z > (9.5-10)/3) = p(z > -0.17) = 0.5675

No more than 5 are delinquent.

P(x =<5 ) = P( x =<5.5) = p( z < (5.5-10)/3) = p(z < -1.5 ) = 0.0668