Economics and Finance. Some of the variables that affect the monthly payment of

Question

Economics and Finance. Some of the variables that affect the monthly payment of a new-car loan are the total amount borrowed, the interest rate, and the length of the loan. During the fourth quarter of 2012, the mean length of a new-car loan was 65 months, a record high according to Experian.

Suppose the length of a new-car loan is approximately normal with standard deviation nine months.

(a) What is the probability ( ±0.0001) that a new-car loan is for at most 46 months?

P(X46) =

(b) What is the probability ( ±0.0001) that a new-car loan length is between 50 and 70 months?

P(50X70) =

(c) Find a symmetrical interval (
±0.0001) about the mean such that 95% of all new-car loan lengths fall in this interval.

Interval : ( , )

(d) Suppose the amount borrowed on a new-car loan is also approximately normal with mean $22000 and standard deviation $5000 . If the length of the loan and the amount borrowed are independent, what is the probability ( ±0.0001) that the loan will be for more than $26000 and for less than 60 months?

P=

Economics and Finance. Some of the variables that affect the monthly payment of a new-car loan are the total amount borrowed, the interest rate, and the length of the loan. During the fourth quarter of 2012, the mean length of a new-car loan was 65 months, a record high according to Experian.

Suppose the length of a new-car loan is approximately normal with standard deviation nine months.

(a) What is the probability ( ±0.0001) that a new-car loan is for at most 46 months?

P(X46) =

(b) What is the probability ( ±0.0001) that a new-car loan length is between 50 and 70 months?

P(50X70) =

(c) Find a symmetrical interval (
±0.0001) about the mean such that 95% of all new-car loan lengths fall in this interval.

Interval : ( , )

(d) Suppose the amount borrowed on a new-car loan is also approximately normal with mean $22000 and standard deviation $5000 . If the length of the loan and the amount borrowed are independent, what is the probability ( ±0.0001) that the loan will be for more than $26000 and for less than 60 months?

P=

Explanation / Answer

Mean = 65
Stdev = 9

a)

P(X<=46)
=P(X<= 46-65 /9)
=P(X<=-2.11)
=1-.9821
=.0179

b)

P(50<X<70)
=P(-1.67<Z<.56)
=.7123-.0475
= .6648

c)

95% CI is +/- 2.575
= 65+/- 2.575*9
41.825,88.175

d)
Mean = 22000
Stdev = 5000
P(Y>26000 and X<60)
=P(Y>26000)*P(X<60)
=P(Z> 26000-22000/5000) *P(Z< 60-65/9)
=P(Z>-.8)*P(Z<-.56)
=.2119*.2877
=.0609

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