PROBLEM 1 -

An economic forecasting organization has developed a model they feel will help them better predict the market conditions than just overall sentiment.  Their proprietary model yields either Positive or Negative ratings that indicate the odds of there being a Good, Fair, or Poor market condition in the future.  At this time, they have tested their model over the past several years and have found that their model has yielded a Positive rating 80% of the time when the market ended up being Good and 60% when it ended up being Fair.  However, Negative ratings were generated 40% and 90% of the time when the market conditions were Fair and Poor, respectively.  In the forecasting organization's analysis, 50% of the market conditions were Good while only 20% of the data represented Poor market conditions.

Perform an analysis for the economic forecasting organization on their model's performance. Show how to depict the model's performance and answer the following probability questions:

1. What is the probability of getting a Positive and Negative rating from the model?

2. P(Positive Rating | Poor Market Condition) = ?

3. P(Negative Rating | Good Market Condition) = ?

4. P(Good Market Condition | Positive Rating) = ?

5. P(Fair Market Condition | Negative Rating) = ?

6. P(Poor Market Condition | Positive Rating) = ?

7. P(Good Market Condition | Negative Rating) = ?

PROBLEM 2 -

The forecasting organization from Problem 1 has decided to try to sell their services to manufacturing firm that are budgeting for the future.  They have been contacted by a potential client that is looking for help in determining whether they should expand their operation for the next year.  They are not certain what the market conditions will be but they have calculated that if the Market conditions are Good, they will generate a profit of $120,000.  If the Market conditions are Fair, they will generate $30,000 and if the Market is Poor then they will lose $60,000.  Also, the manufacturing firm is unsure of the odds of the forecasting firm's Positive and Negative Ratings.

Help the forecasting organization prepare for their consulting pitch to the manufacturing firm.  The forecasting organization needs to make recommendations to the firm about their business options as well as pricing their model's predictive services.  Develop your analytical tool and answer the following business questions:

1. What are the manufacturing firm's options and optimal choices of those options?

 2. What is the value of the forecasting organization's model, at least to the manufacturing firm?

3. How low could the odds for getting a Positive rating go before the model's expected performance is not favorable to the manufacturing firm?

PROBLEM 3 -

There are 4 types of business personalities being examined by a business about their employees, identified as Types Alpha, Beta, Gamma, and Omega.  After an internal sampling of 20 employees, the organization found that there were 4 Type Alphas, 5 Betas, 7 Gammas, and 4 Omegas.  The firm's psychologist has recommended that they should minimize the number of Type Omegas in the firm.

The firm has 500 employees and has the psychologist to determine the following:

1. The expected number of Type Omegas in the firm

2. The probability of there being fewer than 20 Type Omegas in the firm

3. The probability of there being more than 30 Type Omegas in the firm

4. The probability of there being between 36 and 42 Type Omegas in the firm

5. The probability of randomly selecting an employee who is not Type Omega

PROBLEM 4 -

A researcher has collected observational data on a hospital's performance.  She is having some difficulties in analyzing the data and has asked for your expertise.  Since she does not have the raw data but only some summary statistics and other information, such as:

 1. She knows that the number of admissions one standard deviation below the mean is 500

2. The minimum and maximum admissions recorded are 220 and 980, respectively

3. The number of admissions marking the 96th percentile is, rounded, 775

Help your friend in determining the following:

1. The mean

2. The standard deviation

3. Whether the data appear skewed or not (no formal analysis needed)

PROBLEM 5 -

Joel Dean rents flea market kiosks by the month on the weekends.  He sells product that he purchases on consignment by the month to match his rental dates.  If he commits to a single kiosk, he is certain to sell his entire product and generate a profit of $800.  If he rents two kiosks, and the demand supports it, his profit more than doubles to $1,800; however, if the demand is too low, his profit is only $500.  If he rents 3 kiosks and demand is high enough, his profit is $3,000; however, if demand only supports 2 kiosks, his profit is only $700 and if demand only supports 1 kiosk, his profit is $0.  Finally, if he rents 4 kiosks with the appropriate demand level, his profit is $4,000; however, at a demand level for 3 kiosks his profit is $1,500.  If demand is for 2 kiosks, then his profit is $0; and, if demand is for only one kiosk, then his loss is $1,000.

The demand distribution for the next month is 35% for 1 kiosk, 25% for 2 kiosks, 25% for 3 kiosks, and 15% for 4 kiosks. Determine the optimal level of kiosks for Joel to commit to for the next month.