DIRECTIONS: Perform the following calcula�ons in EXCEL, then copy and paste the

DIRECTIONS: Perform the following calcula�ons in EXCEL, then copy and paste the answers in a

WORD document and convert into a PDF file. Upload both the EXCEL File and PDF file. The work will

be graded for completeness, clarity of presenta�on and correctness. This project will count 5% of the

overall grade in the course.

1. UNDERWATER MORTGAGE

Twenty percent of US mortgages are “underwater” (The Boston Globe, March 5, 2009). A mortgage

is considered underwater if the value of the home is less than what is owed on the mortgage.

Suppose 100 mortgage holders are randomly selected.

a) What is the probability that more than 20 of the mortgages are underwater?

b) What is the probability that at least 25 of the mortgages are underwater?

2. CHEATING ON AN EXAM

A professor has learned that three students in her class of 20 will cheat on the exam. She decides to

focus her aten�on on four randomly chosen students during the exam.

a) Find the probability that she finds at least one of the students chea�ng if she focuses on four

randomly chosen students?

b) Find the probability that she finds at least one of the students chea�ng if she focuses on six

randomly chosen students?

3. MPG RATING OF CARS

Suppose that the miles-per-gallon ra�ng of passenger cars is a normally distributed random variable

with a mean of 33.8 mpg and standard devia�on of 3.5 mpg.

a) What is the probability that a randomly selected passenger car gets at least 40 mpg.

b) What is the probability that a randomly selected passenger car gets at most 30 mpg.

c) What is the probability that a randomly selected passenger car gets between 30 and 40 mpg.

d) An automobile manufacturer wants to build a new passenger car with an mpg ra�ng that

improves upon 99% of exis�ng cars. What is the minimum mpg that would achieve this goal?

4. MAXIMIZE RETURN/MINIMIZE RISK

You are considering the risk-return profile of two mutual funds for investment. The rela�vely risky

fund promises an expected return of 8% with a standard devia�on of 14%. The rela�vely less risky

fund promises an expected return of 4% with a standard devia�on of 5%. Assume that the returns

are approximately normally distributes.

a) Which mutual fund you will pick if your objec�ve is to minimize the probability of earning a

nega�ve return?

b) Which mutual fund will you pick if your objec�ve is to maximize the probability of earning a

return above 8%?