Mobile Oil Company

The Mobile Oil company owns land in Alaska that might contain natural oil. The current value of the land is worth $90,000. However, if natural oil is present at the site, the oil will be worth $800,000. If the company decides to extract the oil from the land, the company will have to pay $100,000 in drilling costs.

Before drilling, the company has an option to carry out a seismic survey at the proposed drilling site. If they do not choose to carry out the survey, the company believes that there is a 0.25 probability that the proposed drilling site actually contains natural oil. However, if the company chooses to carry out the survey, the company will have to pay $30,000 for the test to be completed.

If the seismic survey is conducted, there are two possible outcomes. In other words, the survey will show either favorable or unfavorable result that natural oil is present. Based on historic records, if the results are favorable, the probability of hitting oil increases to 0.50. Even if the survey is unfavorable, there is still a chance that natural oil is present. However, if this is the case, the probability of hitting oil reduces to 0.14285.

If Mobile Oil decides not to drill, the company will sell their land at its current value. However, the land is considered worthless if the land is drilled. In addition, if the land has value (i.e. not drilled on), assume that the current value of the land does not change based on the results of the survey.

A summary of the financial parameters is shown below in Table 1, where costs are in terms of thousands of dollars.

Table 1: Financial parameters ($000)

Survey cost

-$30

Drilling cost

-$100

Current value

$90

Oil value

$800

Land value if drilled

$0

1. Develop a decision tree for this problem so that the expected monetary value can be evaluated.

a. HINT: Be sure to reference the tables that have been provided.

b. HINT: You will use the probabilities listed in Table 2 only once in order to develop a decision tree for this problem correctly.

2. Develop a formula that determines the highest expected monetary value that Mobil Oil can anticipate. In addition, develop a formula that will determine the course of action that Mobil Oil will take (i.e. Survey Do not Survey).

Please list out the excel formula's for each. I was not able to include the table for the data when I copied over.

Comments and Hints

Several probabilities are needed in order to construct a decision tree correctly. These probabilities are listed below in Table 2. However, to understand the probabilities that are given to you, please consider the following notation. For example, P(OP) is the probability of oil being present and P(OP|F) is the

probability of oil being present given (i.e. “|” ) that a favorable survey result was obtained. A

description of the abbreviations used in this problem is shown in the list below.

• OP Oil is Present

• ONP Oil is Not Present

• F Favorable Survey

• U Unfavorable Survey

The probabilities that are necessary to fill out the decision tree correctly are shown in the table below.

Table 2: Decision Tree Probabilities

P(OP) 0.25000%

P(ONP) 0.75000%

P(FS) 0.30000%

P(US) 0.70000%

P(OP|FS) 0.50000%

P(OP|US) 0.14285%

P(ONP|FS) 0.50000%

P(ONP|US) 0.85715%

Suppose 31 pregnant women are sampled who smoke an average of 22 cigarettes per day with a variance of 144.00.

a) What is the probability that the pregnant women will smoke an average of 20 cigarettes or more? probability =

b) What is the probability that the pregnant women will smoke an average of 21 cigarettes or less? probability =

c) What is the probability that the pregnant women will smoke an average of 18 to 24 cigarettes? probability =

d) What is the probability that the pregnant women will smoke an average of 23 to 26 cigarettes? probability =

Note: Do NOT input probability responses as percentages; e.g., do NOT input 0.9194 as 91.94.

Programming in C Game of Craps

PR01
The game of craps is often said to be the “fairest” casino game of pure chance (meaning that
there is no player strategy involved) in that the house has the smallest advantage over the
player. What is that advantage? To answer this question we need to first define, precisely, what
we mean by “advantage”. The house advantage is simply the fraction of bets placed that will go
to the house, on average.

To estimate the house advantage for craps perform a Monte Carlo simulation of the game for
many millions of games, keeping track of the total amount bet and the total amount collected
by the house.

The rules of craps are very simple (note that we are not considering “side bets”). A player
places a wager and they will either lose the game (and their wager) or they will win the game
(and get both their wager and an equal payout from the house). Each game consists of a
number of throws of two fair six-sided dice (with sides equal to {1,2,3,4,5,6}. On each roll the
sum of the two dice is calculated. On the first roll, if a player rolls a 7 or an 11 they win
immediately. If the first roll is 2, 3, or 12 they lose immediately. Any other result establishes the
player’s “point” for that game. They then continue rolling the dice until they either roll their
point again (and win) or roll a 7 (and lose).

Write a predicate function that plays a single game of craps and returns TRUE if the player wins
and FALSE if the player loses. On each game place a random bet ranging from $1 to $1000
(whole dollar increments is fine). Collect data not only on the total amount wagered and the
total (net) amount taken by the house, but also aggregate data on how long games last and
their outcome. The end result should be output similar to the following (fake data). Note that
the percentages in parens on each line are the percentage of games that lasted that length, not
the fraction of total games played. The last column is the percentage of all games that lasted
that number of rolls.

GAMES PLAYED:........ 1000000
LONGEST GAME:........ 31 rolls
HOUSE ADVANTAGE:..... 1.734%
ROLLS WON LOST % OF GAMES
1 222222 (66.667%) 111111 (33.333%) 33.333
2 22222 ( 2.222%) 11111 ( 1.111%) 17.234
3 2222 ( 0.222%) 11111 ( 1.111%) 8.645
4 222 ( 0.022%) 1111 ( 0.111%) 0.935
...
20 22 ( 0.002%) 1 ( 0.000%) 0.006
>20 2222 ( 0.222%) 111 ( 0.011%) 0.521

PR02
Take a slightly different look at the game of craps by tabulating the odds of winning (the
fraction of the time that the player wins) for each possible mark value. This table should look
something like:
GAMES PLAYED:........ 1000000
FIRST ROLL WIN:...... 22.222%
FIRST ROLL LOSS:..... 11.111%
POINT WON LOST
4 222222 (22.222%) 111111 (11.111%)
5 22222 (22.222%) 111111 (11.111%)
6 2222 (22.222%) 111111 (11.111%)
8 26 (13.222%) 173 (86.778%)
9 222222 (22.222%) 111111 (11.111%)
10 222222 (22.222%) 111111 (11.111%)

Again, note that the numbers above are just effectively random placeholder values.
The percentages for the first-roll figures should be as a fraction of all games played. The
percentages for the values in the table should be as a fraction of all games that used that row’s
point value. The idea is for the player to know that IF their point is 8, then they have a 13%
change of winning that game – so the percentages on each row should sum to 100%.

2. You are given three solutions to test in the lab: 1.0 M glucose, 1.0 M potassium nitrate, and 1.0 M potassium phosphate. Place the solutions in order from lowest to highest

a. boiling point
b. vapor pressure
c. freezing point

Three taxes: Sales Tax, Property Tax, and Income Tax.

• Name three types of taxes and analyze the deadweight loss of each.
• Which of these taxes do you believe create the highest deadweight loss? Why?
• Why is deadweight loss disagreed on by experts? Explain.

1. Can you identify the level of measurement (nominal, ordinal, interval, or ratio) most likely to be used to quantify the following variables: soda flavors, student class ranking, class exam scores (where lowest score is 1 and highest score is 100), and height?

(answer all three parts} Normal (i.e. average) internal temperature for humans is approximately 98 degrees, If a given population has a standard deviation of 1.2 degrees, what is the maximum temperature for the lowest 35% of the population? What is the minimum temperature for the highest 25% of the population.

PLEASE PLUG IN YOUR OWN VALUES FOR THE GIVEN PROBLEM AND SOLVE:

A projectile is fired with an upward aim from a cliff and lands somewhere away and below the cliff. You are asked to find the vertical distance between where the projectile lands and the highest point in the trajectory of the projectile.

Urgent

XX Company had a beginning inventory on January 1 of 160 units of Product 4-18-15 at a cost of $20 per unit. During the year, the following purchases were made.

1,000 units were sold. XX Company uses a periodic inventory system.

Instructions

(a) Determine the cost of goods available for sale.

(b) Determine (1) the ending inventory, and (2) the cost of goods sold under each of the

assumed cost flow methods (FIFO, LIFO, and average-cost).

(c) Which cost flow method results in (1) the highest inventory amount for the balance

sheet, and (2) the highest cost of goods sold for the income statement?