Risk Management course question.

On Monday, Wile E. is expecting to receive a package (package A) from Acme Distributing containing an anvil valued at $100. Based on his past experience with the delivery service, Wile E. estimates that this package has a 15% chance of being lost in shipment.

1. What is the random variable in this scenario?

2. Is Wile E.’s probability estimate an a priori (theoretical) probability or statistical (empirical) probability? Justify your answer.

3. Create a table and derive the probability distribution for total dollar losses in this case. Note that this is total dollar losses, not number of losses. Make sure you label your table correctly.

4. Is this an example of a compound/joint outcome or mutually exclusive event? Explain why.

5. On Friday, Wile E. expects another package (package B) from Acme Distributing containing dynamite valued at $300. This package has a 20% chance of being lost in shipment.What are the possible outcomes for Wile E.’s total dollar amount of losses for packages A (anvil) and B (dynamite)? For each dollar amount of loss you identify, describe under what circumstances it would occur. In other words, what has to happen in order for each dollar amount of losses to occur? Please note that this asks about total dollar amount of losses, not number of losses.

6. For each of the possible outcomes you identify in #5 above, derive the probability of the outcome occurring. Show calculations.

1. Empirical probability: A statistical model was developed to predict whether passengers on the Titanic ship survived base on their information such as age, number of siblings and spouses were on the ship, sex, the fare class, etc. The table below presents the predicted results getting from the model compared with the actual record:

1. If picking a random passenger, what is the probability that the passenger survived according to the model or predicted by the model?

2. If picking a random passenger, what is the probability that the passenger did not survive according to the real record?

3. If a passenger was predicted as a survivor, what is the probability that the passenger actually survived according to the actual record?

4. If a passenger was predicted as a non-survivor, what is the probability that the passenger actually did not survive according to the actual record?  

2. You are conducting a statistical study in order to estimate the average number of people who have contacted a patient with a positive test for the COVID-19 virus in the US over the last three weeks. Describe a detailed plan for collecting the data for your study. Your answer should be in paragraph​        form and be sure to include the following information:  
   1. The target population
   2. The study variable(s); the variable(s)’s type (quantitative or qualitative); the variable(s)’s level of measurement (nominal, ordinal, interval, or ratio)
   3. The study sample:
      1. Your sample size
      2. Data collection method (survey, simulation, etc)
      3. Sample technique (clustered, stratified, simple random, etc)
      4. Possible errors if any  

write a 500-word essay on your interpretation of the Electoral College map, keeping in mind the candidate who reaches 270 electoral votes wins the presidency. For further discussion, view the 2016 Electoral Map (go to the site and click on the 2016 tap) to understand how citizens voted in the last presidential election. Pay particular interest to “toss up” states. How to you think they will vote and why?

Consider three players (1, 2, 3) and three alternatives (A, B, C). Players vote simultaneously for an alternative and abstention is not allowed.The alternative with more votes wins. If no alternative receives a majority, alternative A is chosen.
U1 (A) = U2 (B) = U3 (C) = 2
U1 (B) = U2 (C) = U3 (A) = 1
U1 (C) = U2 (A) = U3 (B) = 0
Obtain all Nash equilibria in
pure strategies.

The following objects are released simultaneously from rest at the top of a 1.35m long ramp inclined at 3.10 degrees to the horizontal: a solid sphere, a solid cylinder, a hollow cylindrical shell, and a hollow ball.

Which wins the race? The solid Sphere won, I just cant get the positions of the other 3 objects

At the moment the winner reaches the bottom, find the positions of the other three objects.

please explain....

Question 1

Fifteen golfers are randomly selected. The random variable represents the number of golfers who only play on the weekends. For this to be a binomial experiment, what assumption needs to be made?
   The probability of golfing on the weekend is the same for all golfers
   The probability of golfing during the week is the same for all golfers
   All fifteen golfers play during the week
   The probability of being selected is the same for all fifteen golfers
  
Question 2

A survey found that 39% of all gamers play video games on their smartphones. Ten frequent gamers are randomly selected. The random variable represents the number of frequent games who play video games on their smartphones. What is the value of n?
   0.39
   x, the counter
   0.10
   10

Question 3

Thirty-five percent of US adults have little confidence in their cars. You randomly select ten US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly six and then find the probability that it is (2) more than 7.
   (1) 0.069 (2) 0.005
   (1) 0.069 (2) 0.974
   (1) 0.021 (2) 0.005
   (1) 0.021 (2) 0.026
  
Question 4

Say a business wants to know if each salesperson is equally likely to make a sale. The company chooses 5 salespeople and gathers information on their sales experiences. What assumption must be made for this study’s probability results to be used in future binomial experiments?
   That for every 5 salespeople, the probability of making a sale is the same
   That the probability of each salesperson being one of the selected 5 is the same
   That 5% is the correct probability to use in future studies
   That the selected 5 have similar characteristics and sales areas as the other salespeople

Question 5

A soup company puts 12 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled?
   n=36, p=0.97, x=36
   n=36, p=0.97, x=1
   n=12, p=0.36, x=97
   n=12, p=0.97, x=0
  
Question 6

A supplier must create metal rods that are 2.3 inches width to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are the correct width or an incorrect width?
   No, as the probability of being about right could be different for each rod selected
   Yes, all production line quality questions are answered with binomial experiments
   No, as there are three possible outcomes, rather than two possible outcomes
   Yes, as each rod measured would have two outcomes: correct or incorrect
  
Question 7

In a box of 12 pens, there is one that does not work. Employees take pens as needed. The pens are returned once employees are done with them. You are the 5th employee to take a pen. Is this a binomial experiment?
   No, binomial does not include systematic selection such as “fifth”
   No, the probability of getting the broken pen changes as there is no replacement
   Yes, you are finding the probability of exactly 5 not being broken
   Yes, with replacement, the probability of getting the one that does not work is the same
  
Question 8

In a box of 12 pens, there is one that does not work. Employees take pens as needed. The pens are returned once employees are done with them. You are the 5th employee to take a pen. Is this a binomial experiment?
   No, binomial does not include systematic selection such as “fifth”
   No, the probability of getting the broken pen changes as there is no replacement
   Yes, you are finding the probability of exactly 5 not being broken
   Yes, with replacement, the probability of getting the one that does not work is the same
  
Question 9

Sixty-one percent of employees make judgments about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?
   0, 1, 7, 8
   0, 1, 2, 8
   1, 2, 8
   1, 2, 7, 8
  
Question 10

Sixty-eight percent of products come off the line within product specifications. Your quality control department selects 15 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?
   Fewer than 8
   Fewer than 9
   Fewer than 11
   Fewer than 10

Question 11

The probability of a potential employee passing a drug test is 86%. If you selected 12 potential employees and gave them a drug test, how many would you expect to pass the test?
   8 employees
   9 employees
   10 employees
   11 employees
  
Question 12

Off the production line, there is a 3.7% chance that a candle is defective. If the company selected 45 candles off the line, what is the probability that fewer than 3 would be defective?
   0.975
   0.916
   0.768
   0.037

The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of the dinner for two at a local Chinese restaurant. The dinner is valued at $35. Since the fortune cookies were donated to the club, we can ignore the cost of the cookies. The club sold 701 cookies before the drawing.

(a) Lisa bought 22 cookies. What is the probability she will win the dinner for two? (Round your answer to three decimal places.)


What is the probability she will not win? (Round your answer to three decimal places.)


(b) Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? (Round your answer to two decimal places.)
$   

How much did she effectively contribute to the hiking club? (Round your answer to two decimal places.)
$

Despite a slew of controversies and 18 months of constant rioting, President Macron of France has managed to bring his approval rating up to a staggering 27% (Up 1% from when I asked this question last semester). Suppose you were to independently and randomly sample 159 French citizens with replacement and ask them whether or not they approve of President Macron’s performance.

(a) Write down the equation, in terms of x, for the probability a certain number of people x within your sample approve of president Macron.

(b) Is it feasible to use this equation in (a) to compute probabilities?

(c) Can you use an alternative method to approximate the probability of a certain number of people in your sample approve of president Macron? State the conditions which you must meet in order to do so, and whether or not they are met.

(d) If you meet the conditions for approximation in (c), use the approximation to calculate the probability of between 25 and 60 (inclusive) people in your sample approve of president Macron. Be sure to apply the appropriate corrections to your approximation, if needed.

According to the Australian Bureau of Statistics, 70% of all Australian men aged 18 and over are overweight or obese. A student takes a random sample of 20 men aged 18 years and over. A particular variable of interest is the ‘number of men aged 18 and over who are overweight or obese’. Based on the above information answer the following questions:

(a) What is an appropriate model to represent the variable of interest? Write down the parameters of the model and their values, if any.

(b) Discuss how the conditions of the appropriate model are satisfied in the context of the current study.

(c) Find the mean and standard deviation of the number of men aged 18 years and over who are overweight or obese using the parameters of the model.

(d) Find the probability that at least 15 of the men aged 18 years and over are overweight or obese.

(e) Determine the probability that, in a random sample of 100 men aged 18 years or more, 75 or more men are overweight or obese. State and check any assumptions, conditions or rules of thumb that should be considered before performing the calculations to determine this probability.

1. Please find the with the following data set:

standard deviation=  

A new number, 199, is added to the data set above. Please find the new range, sample standard deviation, and IQR of the new data set.

standard deviation =  

2. The length of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 51 and 51.2 min.

P(51 < X < 51.2) =

You must draw a sketch of the distribution, with the area representing the probability you are finding shaded, and all-important values marked on both axes. You also need to show your calculation. Include this sketch and calculation with the work that you upload for the test and be sure to include the question number.

60% of all Americans are homeowners. If 36 Americans are randomly selected, find the probability that

a. Exactly 20 of them are homeowners.
b. At most 22 of them are homeowners.
c. At least 20 of them are homeowners.