Discussion Board Forum 1/Project 2 Instructions

Standard Deviation and Outliers

Thread:

For this assignment, you will use the Project 2 Excel Spreadsheet to answer the questions below. In each question, use the spreadsheet to create the graphs as described and then answer the question.

Put all of your answers into a thread posted in Discussion Board Forum 1/Project 2.

This course utilizes the Post-First feature in all Discussion Board Forums. This means you will only be able to read and interact with your classmates’ threads after you have submitted your thread in response to the provided prompt. For additional information on Post-First, click here for a tutorial. This is intentional. You must use your own work for answers to Questions 1–5. If something happens that leads you to want to make a second post for any of your answers to Questions 1–5, you must get permission from your instructor.

1. A. Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far away from the original 5 and record the new standard deviation.

What is the impact of the new point on the standard deviation? Do not just give a numerical value for the change. Explain in sentence form what happened to the standard deviation. (4 points)

B. Create a data set with 8 points in it that has a mean of approximately 10 and a standard deviation of approximately 1. Use the second chart to create a second data set with 8 points that has a mean of approximately 10 and a standard deviation of approximately 4. What did you do differently to create the data set with the larger standard deviation? (4 points)

2. Go back to the spreadsheet and clear the data values from Question 1 from the data column and then put values matching the following data set into the data column for the first graph. (8 points)

50, 50, 50, 50, 50.

Notice that the standard deviation is 0. Explain why the standard deviation for this one is zero. Do not show the calculation. Explain in words why the standard deviation is zero when all of the points are the same. If you don’t know why, try doing the calculation by hand to see what is happening. If that does not make it clear, try doing a little research on standard deviation and see what it is measuring and then look again at the data set for this question.

3. Go back to the spreadsheet one last time and put each of the following three data sets into one of the graphs. Record what the standard deviation is for each data set and answer the questions below.

                  Data set 1:       0, 0, 0, 100, 100, 100

                  Data set 2:       0, 20, 40, 60, 80, 100

                  Data set 3:       0, 40, 45, 55, 60, 100

Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists. Do not give your calculations in your answer—explain in sentence form. (8 points)

For the last 2 questions, use the Project 1 Data Set.

4. Explain what an outlier is. Then, if there are any outliers in the Project 1 Data Set, what are they? If there are no outliers, say no outliers. (4 points)
5. Which 4 states have temperatures that look to be the most questionable or the most unrealistic to you? Explain why you selected these 4 states. For each state, give both the name and the temperature. (4 points)

An earthquake P wave traveling at 7.7km/s strikes a boundary within the Earth between two kinds of material.

If it approaches the boundary at an incident angle of 44? and the angle of refraction is 33?, what is the speed in the second medium?

Express your answer to two significant figures and include the appropriate units.

1. Friedman Manufacturing, Inc. has prepared the following information regarding two investments under consideration. Which investment is better, based on risk (as measured by the standard deviation) and return?

2. “ More can be said about risk, especially as to its nature, when we own more than one asset in our investment portfolio.” Define risk and explain how risk is affected if we diversify our investment by holding a variety of securities?

suppose that you encounter two traffic lights on your commute to school. Based on past experience, you judge that the probability is .60 that the first light will be red when you get to it, .50 that the second light will be red, and .40 that both lights will be red.

a)Determine the conditional probability that the second light will be red, given that the first light is red. (Here and throughout, show the details of your calculations.)

b)Are the events {first light is red} and {second light is red} independent? Justify your answer.

c) Given that at least one light is red, what is the probability that both lights are red? (Show your work.)

Objective: To practice identifying dynamic complexity.Instructions: Describe how the following example illustrates one or more of the system characteristics that contribute to dynamic complexity.Example: Medical Associates is a for-profit medical group of 40 physicians that operates two facilities and offers services in several medical specialties, including cardiology; ear, nose, and throat; family medicine; gastroenterology; general surgery; pediatrics; and obstetrics and gynecology. Medical Associates is open six days a week in each location from 8:00 am until 6:00 pm. Plans are being developed to extend its hours to 9:00 pm two days a week. For several years, Medical Associates discounted its listed fees by 3 percent to 5 percent

VIII. Regarding the data offered in problem VII, we are interested in identifying which is the best statistical relationship between the variables considered.

Using all the information previously obtained by you I analyzed:

(1) the correlation coefficients, identifying which is the best and the weakest among all the possible regressions and equations.
(2)  the regression errors obtained, identifying which is the best and the weakest among all the possible regressions and equations.
(3) the required hypothesis tests

-(4) Present and identify which is the best equation to predict the monthly average purchase volume, explain why it is the best equation.

(5) With the best estimated equation present the confidence interval to predict the monthly average purchase volume, when the Area of
the store is 585, the family income is 50,000 and the parking number is 10.

A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the table below. Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand: P (low) = .3 and P (high) = .7.

* Profit in $ thousands.

a-1. Determine the expected profit of each alternative. (Enter your answers in thousands. Omit the "$" sign in your response.)

a-2. Which alternative is best?

• Do nothing

• Expand

• Subcontract

c. Compute the expected value of perfect information. (Enter your answers in thousands. Omit the "$" sign in your response.)

EVPI           $  thousands

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A fair coin is tossed 7 times. Compute the probability of tossing 7 tails in a row.
1128​  
Enter your response as a reduced fraction.

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Unattempted Question 2

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A CEO of Awesome Coolers owns 4 pairs of pants, 13 shirts, 8 ties and 3 jackets. How many different outfits can he wear to the office if he must wear one of each item?

The CEO has  different outfits.

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Unattempted Question 3

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In a large population, 65 % of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?

Give your answer as a decimal (to at least 3 places) or fraction.   

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Unattempted Question 4

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Given the probability of an event is 110110, what are the odds against that event?

:

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Unattempted Question 5

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A student's grades and weights are given below. Calculate the final grade by calculating a weighted average.

Calculate the student's final grade:  %

Round your answer to one decimal place.

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Unattempted Question 6

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A person must pay $$4 to play a certain game at the casino. Each player has a probability of 0.01 of winning $$16, for a net gain of $$12 (the net gain is the amount won 16 minus the cost of playing 4).

Each player has a probability of 0.99 of losing the game, for a net loss of $$4 (the net loss is simply the cost of playing since nothing else is lost).

What is the Expected Value for the player (that is, the mean of the probabiltiy distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer with two decimal places.

Expected Value = $

If a person plays this game a very large number of times over the years, do we expect him/her to come out financially ahead or behind?

• behind
• ahead

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Unattempted Question 7

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A 10-sided fair die, a 4-sided fair die, and a 6-sided fair die are rolled. What is the probability of all three happening:

• Showing 3 on the first die
• Showing either 3 or 4 on the second die
• Showing an odd number on the third die

Probability =   
(Enter your answer as a reduced fraction.)

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Unattempted Question 8

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A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected:

One customer is chosen at random for a prize giveaway.

What is the probability that the customer is at least 30 but no older than 50?   

What is the probability that the customer is either older than 60 or younger than 40?   

What is the probability that the customer is at least 60?   

Enter your answers as either decimals or fractions, not as percents.

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Unattempted Question 9

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Frank earned the following grades last quarter. Calculate his GPA rounded to two decimals.

GPA:

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Unattempted Question 10

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The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their car.

If one person is randomly selected from the group, what is the probability that this person drives a red car or did not get a speeding ticket?

Probability =   

(Enter your answer as a reduced fraction.)

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Unattempted Question 11

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A company has 4 mechanics and 9 electricians. If an employee is selected at random, what is the probability that they are an electrician?

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Unattempted Question 12

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Eleven bands are to perform at a weekend festival. How many different ways are there to schedule their appearances?

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Unattempted Question 13

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Based on historical data, an insurance company estimates that a particular customer has a 2.4% likelihood of having an accident in the next year, with the average insurance payout being $2300.

If the company charges this customer an annual premium of $150, what is the company's expected value of this insurance policy?

$  

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Unattempted Question 14

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Evaluate the following.

23C723C7 =

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Unattempted Question 15

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A jury pool consists of 34 people, 16 men and 18 women. Compute the probability that a randomly selected jury of 12 people is all male.

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Unattempted Question 16

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A bag of M&M's has 8 red, 5 green, 2 blue, and 4 yellow M&M's. What is the probability of randomly picking:

(give answer as a reduced fraction)

1) a yellow?

  

2) a blue or green?

  

3) an orange?

  

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Unattempted Question 17

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A race consists of 12 women and 11 men. Find the following probabilities for the top three finishers:

P(all men) =   

P(all women) =   

P(2 men and 1 woman) =   

P(1 man and 2 women) =   

Round all answers to four decimal places.

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Unattempted Question 18

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A card is drawn randomly from a standard 52-card deck. Find the probability of the given event.
(a) The card drawn is 5
The probability is :   

(b) The card drawn is a face card (Jack, Queen, or King)
The probability is :   

(c) The card drawn is not a face card.
The probability is :   

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Unattempted Question 19

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Suppose a jar contains 10 red marbles and 32 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.

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Unattempted Question 20

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Michael buys a bag of cookies that contains 5 chocolate chip cookies, 5 peanut butter cookies, 5 sugar cookies and 9 oatmeal cookies. What is the probability that Michael randomly selects an oatmeal cookie from the bag, eats it, then randomly selects a chocolate chip cookie? Express you answer as a reduced fraction.

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Unattempted Question 21

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Eight sprinters have made it to the Olympic finals in the 100-meter race. Suppose you want to determine how many different ways the gold, silver, and bronze medals can be awarded. Would you use a combination or a permtuation?

• Combination
• Permutation

CHOOSE THE CORRECT AMSWER

5.   There are several steps for the Critical Decision-Making Model. These steps would include all of the following except:

1. Act, Review and Re-assign
2. Consider Powers and Policy
3. Collect Information and Intelligence
4. Identify Options and Determine Best Course of Action

6.   Which of the following requires the preparation of a Complaint Report Worksheet

1. A civilian wish to make an allegation of corruption against a police officer
2. A civilian wish to make a complaint against a Traffic Enforcement Agent
3. A woman hands you a wallet and said that she found it on the ground
4. A man asks you if you could help him, because he lost his wallet

7. Which of the following tasks is not necessary for conducting a preliminary investigation?

A.    Make notes in an activity log

B.     Identify, isolate, and interview any victims, complaints, and witnesses

C.    Rely solely on your memory

D.    Make a probable cause determination

8.   The Police Department has categorized serious felonies according to the “7 Major Felony” rule. Which of the following would be considered the most serious charge according to the rule?

1. Attempted Murder
2. Rape
3. Robbery
4. Felonious Assault

9. Complainant walks into 50 Pct (Bronx) and would like to make a report for lost property which occurred in the 60 Pct (Brooklyn). Complainant is greeted by Cadet Tsui in the Pct, which statement is most accurate for Cadet Tsui to assist the complainant?

1. Refer the complainant to the 60 Pct
2. Prepare a complaint report worksheet
3. Have complainant report back to the location where the property was lost and call 911
4. Telephone the 60 Pct to request a UMOS assigned to the 60 Pct to come to 50 Pct to take a report

10. According to the Investigation and Report Writing Chapter, which statement is most accurate?

1. Member of service will not take a report if the complainant is unwilling to prosecute the offender
2. Member of service will not take a report if the complainant is unable to provide receipts for property reported stolen
3. Member of service will not take a report if complainant refuses to return to command and speak with detectives
4. Member of service may not direct a complainant to go to a precinct, police service area, or transit district merely to have an initial report prepared

THANK YOU

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%.