UI STAT 251 Fall 2010 Quiz 10 NAME: UI #: Class: 9:30
Based on past experience, a bank believes that 8% of the people who receive loans will not make timely payments. The bank has recently approved 140 loans.
a. What are the mean and standard deviation of the proportion of clients in this group who may not make timely payments?
b. What assumptions underlie your model? Are the conditionals met? Explain.
c. What’s the probability that under 3% of these clients will not make timely payments?
a)
μp=p=0.08
σp=pqn=0.08*0.92140=0.023
b)
Randomization condition: Assume that the 140 people are a representative sample of all loan recipients. It is random.
10% condition: 140 is less than 10% of all loan recipients.
Success/Failure condition: np=11.2 nq=128.8 are both greater than 10.
So, the sampling distribution model for the proportion of 140 loan recipients tho will not make payments on time is N(0.08,0.023)
c)
Z=p-μpσp=0.03-0.080.023=-2.17
> pnorm(-2.17)
[1] 0.01500342
P=0.015
UI STAT 251 Fall 2010 Quiz 10 NAME: UI #: Class: 10:30
Based on past experience, a bank believes that 10% of the people who receive loans will not make timely payments. The bank has recently approved 140 loans.
a.What are the mean and standard deviation of the proportion of clients in this group who may not make timely payments?
b.What assumptions underlie your model? Are the conditionals met? Explain.
c.What’s the probability that under 3% of these clients will not make timely payments?
a)
μp=p=0.1
σp=pqn=0.1*0.9140=0.025
b)
Randomization condition: Assume that the 140 people are a representative sample of all loan recipients. It is random.
10% condition: 140 is less than 10% of all loan recipients.
Success/Failure condition: np=14 nq=126 are both greater than 10.
So, the sampling distribution model for the proportion of 140 loan recipients tho will not make payments on time is N(0.08,0.023)
c)
Z=p-μpσp=0.03-0.10.025=-2.8
> pnorm(-2.8)
[1] 0.002555130
P=0.0026