Example 1:Suppose that your wife is pregnant and due in 100 days. Suppose that the probability density distribution function for having a child is approximately normal with mean 100 and standard deviation 8. You have a business trip and will return in 85 days and have to go on another business trip in 107 days.

A. What is the probability that the birth will occur before your second trip?

B. What is probability that the birth will occur after you return from your first business trip?

C. Given that the baby will be born after the first business trip, what is the probability that you will be there for the birth?

D. You are able to cancel your second business trip, and your boss tells you that you can return home from your first trip so that there is a 99% chance that you will make it back for the birth. When must you return home?

E.         P(z < .88) = .50+.3106=.8106F.         P(z > -1.88)=.50+.4699=.9699

G. P( -1.88<z <.88 I z>-1.88)=.4699+.3106= .7805/.9699=.8047

H. X= 100-2.33*8=81.36

I.

Example 2

Graduate Management Aptitude Test (GMAT) scores are widely used by graduate schools of business as an entrance requirement. Suppose that in one particular year, the mean score for the GMAT was 476, with a standard deviation of 107. Assuming that the GMAT scores are normally distributed, What is the probability of receiving a score between 440 and 330 on a GMAT test.

P(-1.36<Z<-.34)=0.28

Example 3

Suppose that a tire factory wants to set a mileage guarantee on its new model called LA 50 tire. Life tests indicated that the mean mileage is 47,900, and standard deviation of the normally distributed distribution of mileage is 2,050 miles. The factory wants to set the guaranteed mileage so that no more than 5% of the tires will have to be replaced. What guaranteed mileage should the factory announce?

X=47,900-1.645(2,050)= 44,528 miles