Please answer A B and C 1 Based on past experience a bank be

Please answer A, B, and C 1) Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans.

a) What are the sample proportion and standard error of the proportion of clients in this group who may make timely payments?

b) What assumptions underlie your model? Are the conditions met?

c) What is the probability that over 10% of these clients will not make timely payments?

Solution

a)
Proportion ( P ) =0.07
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.07*0.93/200)=0.018
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
c)
P(X > 0.1) = (0.1-0.07)/0.018
= 0.03/0.018 = 1.6667
= P ( Z >1.667) From Standard Normal Table
= 0.0478