Question

The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of $76,000 and a standard deviation of $20,000. A loan application is received this morning. What is the probability that: (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.) a. The amount requested is $85,000 or more? Probability b. The amount requested is between $67,000 and $85,000? Probability c. The amount requested is $67,000 or more? Probability

Answer 1

(a)

= 76,000

= 20,000

To find P(X85,000):

Z = (85,000 - 76,000)/20,000 = 0.45

Table of Area Under Standard Normal curve gives area= 0.1736

So,

P(X85,000) = 0.5 - 0.1736 = 0.3264

So,

Answer is:

0.3264

(b)

= 76,000

= 20,000

To find P(67,000 <X<85,000):

Case 1: For X from 67,000 to mid value:

Z = (67,000 - 76,000)/20,000 = - 0.45

Table of Area Under Standard Normal curve gives area= 0.1736

Case 2: For X from mid value to 85,000:

Z = (85,000 - 76,000)/20,000 = 0.45

Table of Area Under Standard Normal curve gives area= 0.1736

So,

P(67,000<X<85,000) = 2 X 0.1736 = 0.3472

So,

Answer is:

0.3472

(c)

= 76,000

= 20,000

To find P(X67,000):

Z = (67,000 - 76,000)/20,000 = - 0.45

Table of Area Under Standard Normal curve gives area= 0.1736

So,

P(X67,000) = 0.5 + 0.1736 = 0.6736

So,

Answer is:

0.6736