Question

The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, where the amount requested for home loans followed the normal distribution with a mean of $62,000 and a standard deviation of $20,000. (Round z-score computation to 2 decimal places and the final answers to the nearest whole dollars.)

a. What is the minimum amount requested on the largest 7% of loans?

$

b. What is the maximum amount requested on the smallest 13% of loans?

$

Answer 1

Part a)

P ( X > ? ) = 1 - P ( X < ? ) = 1 - 0.07 = 0.93
Looking for the probability 0.93 in standard normal table to calculate critical value Z = 1.48

1.48 = ( X - 62000 ) / 20000
X = 91600
P ( X > 91600 ) = 0.07

Part b)

P ( X < ? ) = 13% = 0.13
Looking for the probability 0.13 in standard normal table to calculate critical value Z = -1.13

-1.13 = ( X - 62000 ) / 20000
X = 39400
P ( X < 39400 ) = 0.13