Question

The amounts of money requested in home loan applicant at Benton County Savings and Loan in Paris, TN are normally distributed with a mean of 75000 and a standard deviation of 15000. A loan application is received in the morning. What is the probability tthat

A. The amount requested is more than 83,000

B. 15% of the loan are larger than what amount

Answer 1

Solution :

Given that,

mean = = 75000

standard deviation = =15000

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

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

= 1 - P(z <0.53 )

Using z table

= 1 -  0.7019

probability= 0.2981

b.

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 * +

=1.04*15000+75000

=90600