Question

The amounts of money requested in home loan applicants at Benton County                       
Savings and Loan in Paris, TN are normally distributed with a mean of $75,000                      
and a standard deviation of $15,000. A loan application is received this morning.                      
What is the probability that:                      
a. The amount requested is more than $83,000?                        
b. 15 percent of the loan are larger than what amount?                  
   Use the Norm.Inv function   
           #N/A          
                      

Answer 1

Solution :

Given that ,

mean = = 75000

standard deviation = = 15000

a) P(x > 83000) = 1 - p( x< 83000)

=1- p P[(x - ) / < (83000 - 75000) / 15000 ]

=1- P(z < 0.53)

Using z table,

= 1 - 0.7019

= 0.2981

b) Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15  

= P(Z < z) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.04 ) = 0.85  

z = 1.04

Using z-score formula,

x = z * +

x = 1.04 * 15000 + 75000

x = $ 90,600