Question

1. The amounts of money requested in home loan applications at Down River Federal Savings, are approximately normally distributed with a mean of $ 700,000 and a standard deviation of $ 200,000. A loan application is received this morning. What is the probability that:
a. The amount requested is $ 800,000 or more?
b. The amount requested is between $ 650,000 and $ 800,000?
c. The amount requested is $ 650,000 or more?
d. Twenty percent of the loans are larger than what amount?

2. Suppose there was a recent article in Newswatch Magazine which stated that the mean amount of leisure time per week for men is 50 hours. You believe this figure is too large and decide to conduct your own test. In a random sample of 58 men, you find out that  
the mean is 48.2 hours of leisure per week and that the standard deviation of the sample is 10 hours. At 0.05 level of significance, can you conclude that the information in the article is untrue?

Answer 1

Given:

= $700,000, = $200,000

a) Find P(X 800,000)

b) P(650,000 < X < 800,000)

C) P(X 650,000)

d)

Find the Z-value with a left tail of 80%

Z(0.80) = 0.8416 ......................From Normal table

Therefore the corresponding loan value using X = + Z

X = + Z

X = 700,000 + 200,000 * 0.8416

X = $ 868324.2