# What is the probability that this woman has no children, given that she works part time?

1. The Wall Street Journal CEO Compensation Study analyzed CEO pay for many U.S. companies with fiscal year 2008 revenue of at least \$5 billion that filed with their proxy statements between October 2008 and March 2009. The data are in the file Mid-Term Exam Q1.
a. Create histograms to gain a clearer understanding of the distribution of annual base salaries and bounces earned by the surveyed CEOs in fiscal 2008. How would you characterize these histograms?
b. Find the annual salary below which 75% of all given CEO salaries fall.
c. Find the annual bonus above which 55% of all given CEO bonuses fall.
2. Consider an individual selected at random from a sample of 750 married women (data is provided in the file Mid-Term Exam Q2) in answering each of the following questions.
a. What is the probability that this woman does not have work outside the home, given that she has at least one child?
b. What is the probability that this woman has no children, given that she works part time?
c. What is the probability that this woman has at least two children, given that she does not work full time?
3. Assume the annual mean return on ABC stock is around 15% and the annual standard deviation is around 25%. Assume the annual and daily returns on ABC stock are normally distributed.
a. What is the probabibility that ABC will lose money during a year?
b. There is a 5% chance that ABC will earn a return of at least what value during a year?
c. There is a 10% chance that ABC will earn a return of less than or equal to what value during a year?
d. What is the probability that ABC will earn at least 35% during a year?
e. Assume there are 252 trading days in a year. What is the probability that ABC will lose money on a given day?
4. Techware Incorporated is considering the introduction of two new software products to the market. The company has four options regarding these two proposed products: introduce neither product, introduce product 1 only, introduce product 2 only, or introduce both products. Research and development costs for products 1 and 2 are \$180,000 and \$150,000, respectively. Note that the first option entails no costs because research and development efforts have not yet begun. The success of these software products depends on the trend of the national economy in the coming year and on the consumers’ reaction to these products. The company’s revenues earned by introducing product 1 only, product2 only, or both products in various states of the national economy are given in the file Final Exam Q4. The probabilities of observing a strong, fair, or weak trend in the national economy in the coming year are assessed to be 0.30, 0.50, and 0.20, respectively.
a. Create a payoff table that specifies Techware’s net revenue (in dollars) for each possible decision and each outcome with respect to the trend in the national economy.