Please work alone in completing this assignment. If you have any questions you may contact me. Be certain to include your Excel output for those questions that use it. See text for information on how to use the Excel functions Binom.Dist and Norm.Dist.
Problem #1 - Probability (No Excel needed):
Since the fall of 2008, millions of Americans have lost jobs due to the economic meltdown. A recent study shows that unemployment has not impacted white-collar and blue-collar workers equally (Newsweek, April 20, 2009). According to the Bureau of Labor Statistics report, while the national unemployment rate is 8.5%, it is only 4.3% for those with a college degree. It is fair to assume that 27% of people in the labor force are college educated. (Hint: This question deals with conditional probabilities and their formulas. Also, remember that probabilities are relative frequencies. So, for example, the national unemployment rate is a relative frequency (the percentage of the labor force unemployed)).
a) Construct a contingency table of probabilities that has college educated (or not) as columns and unemployed (or not) as rows.
b) You have just heard that another worker in a large firm has been laid off (unemployed). What is the probability that the worker is college educated?
c) What is the probability that a worker is unemployed and not college educated?
d) What is the probability that a worker is either employed or college educated? Show your work. You will not get full credit if you just put down an answer with no supporting material.
Problem #2 - Expected Value. (No Excel needed):
You are considering buying insurance for your new laptop computer, which you have recently bought for $1,500. The insurance premium for three years is $80. Over the three-year period there is an 8% chance that your laptop computer will require work worth $400, a 3% chance that it will require work worth $800, and a 2% chance that it will completely break down with a scrap value of $100 and thus you will lose ($1,500-$100) = $1,400. Should you buy the insurance based on expected values (your expected loss)?
Problem #3 - Binomial RV (Use Excel's Binom.Dist. function, and show your work including the parameters you used )
Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack.
a) What is the probability that a single detection system will detect an attack? Now.. suppose that four systems are installed.
b) Explain how you would set this up as a binomial discrete random variable (e.g. what is the random variable, what are the number of trials (n), what is the probability of success on each trial).
c) Use Binom.Dist to answer the following (show your work, including the Binom.Dist functions you used).
i) What is the probability that at least one of the systems will detect an attack? Explain your answer and show your work.
ii) What is the probability that all four of the systems will detect an attack?
d) Would you recommend that multiple detection systems be used? Why?
e) What is the expected number of systems that will detect an attack successfully?
Problem #4 - Normal Distribution (Use Excel (Norm.Dist) to provide your answers)
The breaking strength of plastic bags used for packaging produce is a continuous random variable which is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch. What is the probability that the bags will have a breaking strength of
a. Less than 3.17 pounds per square inch?
b. Between 5 and 5.5 pounds per square inch?
c. At least 3.6 pounds per square inch.