The manufacturer of a certain electronic component claims that they are designed to last just slightly more than 4 years because they believe that customers typically replace their device before then. Based on information provided by the company, the components should last a mean of 4.24 years with a standard deviation of 0.45 years. For this scenario, assume the lifespans of this component follow a normal distribution.

1. The company offers a warranty for this component that allows customers to return for a refund it if it fails in less than 4 years. What is the probability that a randomly chosen component will last less than 4 years?

2.The company considers a component to be “successful” if it lasts longer than the warranty period before failing. They estimate that about 70.3% of components last more than 4 years. They find a random group of 10 components that were sold and count the number of them which were “successful,” lasting more than 4 years.

What is the probability that at least 8 of these components will last more than 4 years?

Does crime pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solved†. Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetrated by the same criminals. The police are investigating three property crime cases in this district.

(a) What is the probability that none of the crimes will ever be solved? (Round your answer to three decimal places.)


(b) What is the probability that at least one crime will be solved? (Round your answer to three decimal places.)


(c) What is the expected number of crimes that will be solved? (Round your answer to two decimal places.)
crimes

What is the standard deviation? (Round your answer to two decimal places.)
crimes

(d) How many property crimes n must the police investigate before they can be at least 90% sure of solving one or more cases?
n = crimes

Let us suppose that some article studied the probability of death due to burn injuries. The identified risk factors in this study are age greater than 60 years, burn injury in more than 40% of body-surface area, and presence of inhalation injury. It is estimated that the probability of death is 0.003, 0.03, 0.33, or 0.84, if the injured person has zero, one, two, or three risk factors, respectively. Suppose that three people are injured in a fire and treated independently. Among these three people, two people have one risk factor and one person has three risk factors. Let the random variable X denote number of deaths in this fire. Determine the cumulative distribution function for the random variable.

Round your answers to five decimal places (e.g. 98.76543).

F(x)=              with x < 0

F(x)=              with 0 <= x < 1

F(x)=              with 1 <= x < 2

F(x)=              with 2 <= x < 3

F(x)=              with 3 <= x

4. Consider two stocks with returns ?_A and ?_B with the following properties. ?_A takes values -10 and +20 with probabilities 1/2. ?_B takes value -20 with probability 1/3 and +50 with probability 2/3. ????(?_A,?_B) = ? (some number between -1 and 1). Answer the following questions

   1. (a) Express C??(?_A,?_B) as a function of ?

   2. (b) Calculate the expected return of a portfolio that contains share ? of stock ? and

      share 1 − ? of stock ?. Your answer should be a function of ?

   3. (c) Calculate the variance of the portfolio from part ? (Hint: returns are now potentially dependent)

   4. (d) What value of ?* minimizes the variance of the portfolio? Your answer should be a function of ?, denoted by ?*(?).

5. (e) For what range of values for ? is your ?*(?) ≤ 1? What is the solution to the above problem if ? is outside of that range? (Hint: draw a graph and nd ?* ∈ [0, 1] that minimizes variance)

6. (f) Is ?*(?) increasing or decreading? (Hint: take the derivative with respect to ?)

7. (g) Which ? would the investor prefer to have, positive or negative? What is the intuition for that result?

Good Time Company is a regional chain department store. It will remain in business for one more year. The probability of a boom year is 60 percent and the probability of a recession is 40 percent. It is projected that the company will generate a total cash flow of $195 million in a boom year and $86 million in a recession. The company's required debt payment at the end of the year is $120 million. The market value of the company’s outstanding debt is $93 million. The company pays no taxes.

a. What payoff do bondholders expect to receive in the event of a recession? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole number, e.g., 1,234,567.)

b. What is the promised return on the company's debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

c. What is the expected return on the company's debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good, and fair categorical scale. Assume the sample data for 200 respondents below applies to this study.

(a)

Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company.

State the null and alternative hypotheses.

H₀: Quality of management is independent of the reputation of the company.
H_a: The proportion of companies with excellent management is equal across companies with differing reputations.H₀: Quality of management is independent of the reputation of the company.
H_a: Quality of management is not independent of the reputation of the company.    H₀: Quality of management is not independent of the reputation of the company.
H_a: The proportion of companies with excellent management is not equal across companies with differing reputations.H₀: Quality of management is not independent of the reputation of the company.
H_a: Quality of management is independent of the reputation of the company.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that the ratings for the quality of management and the reputation of the company are not independent.Reject H₀. We conclude that the rating for the quality of management is not independent of the rating for the reputation of the company.     Do not reject H₀. We cannot conclude that the rating for the quality of management is independent of the rating of the reputation of the company.Reject H₀. We conclude that the rating for the quality of management is independent of the rating for the reputation of the company.

(b)

If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.

For companies with an excellent reputation, the largest column probability corresponds to  ---Select--- excellent good fair management quality. For companies with a good reputation, the largest column probability corresponds to  ---Select--- excellent good fair management quality. For companies with a fair reputation, the largest column probability corresponds to  ---Select--- excellent good fair management quality. Since these highest probabilities correspond to  ---Select--- the same different ratings of quality of management and reputation, the two ratings are  ---Select--- associated independent .

The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good, and fair categorical scale. Assume the sample data for 200 respondents below applies to this study.

Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company.

A) State the null and alternative hypotheses.

H₀: Quality of management is independent of the reputation of the company.
H_a: Quality of management is not independent of the reputation of the company.

H₀: Quality of management is not independent of the reputation of the company.
H_a: Quality of management is independent of the reputation of the company.    

H₀: Quality of management is not independent of the reputation of the company.
H_a: The proportion of companies with excellent management is not equal across companies with differing reputations.

H₀: Quality of management is independent of the reputation of the company.
H_a: The proportion of companies with excellent management is equal across companies with differing reputations.

B) Find the value of the test statistic. (Round your answer to three decimal places.)

C) Find the p-value. (Round your answer to four decimal places.)

D) State your conclusion.

Do not reject H₀. We cannot conclude that the rating for the quality of management is independent of the rating of the reputation of the company.

Reject H₀. We conclude that the rating for the quality of management is not independent of the rating for the reputation of the company.     

Reject H₀. We conclude that the rating for the quality of management is independent of the rating for the reputation of the company.

Do not reject H₀. We cannot conclude that the ratings for the quality of management and the reputation of the company are not independent.

E) If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.

For companies with an excellent reputation, the largest column probability corresponds to [ EXCELLENT/GOOD/FAIR ] excellent good fair management quality. For companies with a good reputation, the largest column probability corresponds to [ EXCELLENT/GOOD/FAIR ] excellent good fair management quality. For companies with a fair reputation, the largest column probability corresponds to [ EXCELLENT/GOOD/FAIR ] excellent good fair management quality. Since these highest probabilities correspond to [THE SAME/DIFFERENT ] the same different ratings of quality of management and reputation, the two ratings are [ ASSOCIATED/INDEPENDENT ] associated independent.

Project 3 instructions

Based on Brase & Brase: sections 6.1-6.3

Visit the NASDAQ historical prices weblink. First, set the date range to be for exactly 1 year ending on the Monday that this course started. For example, if the current term started on April 1, 2018, then use April 1, 2017 – March 31, 2018. (Do NOT use these dates. Use the dates that match up with the current term.) Do this by clicking on the blue dates after “Time Period”. Next, click the “Apply” button. Next, click the link on the right side of the page that says “Download Data” to save the file to your computer. NOTE THIS CLASS BEGAN ON 1/20/2020 please use this date to help me answer these questions... I am having a hard time

This project will only use the Close values. Assume that the closing prices of the stock form a normally distributed data set. This means that you need to use Excel to find the mean and standard deviation. Then, use those numbers and the methods you learned in sections 6.1-6.3 of the course textbook for normal distributions to answer the questions. Do NOT count the number of data points.

Complete this portion of the assignment within a single Excel file. Show your work or explain how you obtained each of your answers. Answers with no work and no explanation will receive no credit.

1. a) Submit a copy of your dataset along with a file that contains your answers to all of the following questions.

b) What the mean and Standard Deviation (SD) of the Close column in your data set?

c) If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: You do not want to calculate the mean to answer this one. The probability would be the same for any normal distribution. (5 points)

2. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at more than $1150? (5 points)
3. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $50 of the mean for that year? (between 50 below and 50 above the mean) (5 points)
4. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than $950 per share. Would this be considered unusal? Use the definition of unusual from the course textbook that is measured as a number of standard deviations (5 points)
5. At what prices would Google have to close in order for it to be considered statistically unusual? You will have a low and high value. Use the definition of unusual from the course textbook that is measured as a number of standard deviations. (5 points)
6. What are Quartile 1, Quartile 2, and Quartile 3 in this data set? Use Excel to find these values. This is the only question that you must answer without using anything about the normal distribution. (5 points)
7. Is the normality assumption that was made at the beginning valid? Why or why not? Hint: Does this distribution have the properties of a normal distribution as described in the course textbook? Real data sets are never perfect, however, it should be close. One option would be to construct a histogram like you did in Project 1 to see if it has the right shape. Something in the range of 10 to 12 classes is a good number. (5 points)

There are also 5 points for miscellaneous items like correct date range, correct mean, correct SD, etc.

Project 3 is due by 11:59 p.m. (ET) on Monday of Module/Week 5.

PROJECT 3 INSTRUCTIONS Based on Brase & Brase: sections 6.1-6.3 Visit the NASDAQ historical prices weblink. First, set the date range to be for exactly 1 year ending on the Monday that this course started. For example, if the current term started on January 13, 2019, then use January 13, 2019 – January 12, 2020. (Do NOT use these dates. Use the dates that match up with the current term.) Do this by clicking on the blue dates after “Time Period”. Next, click the “Apply” button. Next, click the link on the right side of the page that says “Download Data” to save the file to your computer. NOTE I’M TO USE THESE DATES: JAN 13, 2019 – JAN 12, 2020. PLEASE USE THESE DATES TO HELP ME ANSWER QUESTIONS # 5 – 7 This project will only use the Close values. Assume that the closing prices of the stock form a normally distributed data set. This means that you need to use Excel to find the mean and standard deviation. Then, use those numbers and the methods you learned in sections 6.1-6.3 of the course textbook for normal distributions to answer the questions. Do NOT count the number of data points. Complete this portion of the assignment within a single Excel file. Show your work or explain how you obtained each of your answers. Answers with no work and no explanation will receive no credit. 1. a) Submit a copy of your dataset along with a file that contains your answers to all of the following questions. b) What the mean and Standard Deviation (SD) of the Close column in your data set? c) If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: You do not want to calculate the mean to answer this one. The probability would be the same for any normal distribution. (5 points) 2. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at more than $1150? (5 points) 3. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $50 of the mean for that year? (between 50 below and 50 above the mean) (5 points) 4. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than $950 per share. Would this be considered unusal? Use the definition of unusual from the course textbook that is measured as a number of standard deviations (5 points)

5. At what prices would Google have to close in order for it to be considered statistically unusual? You will have a low and high value. Use the definition of unusual from the course textbook that is measured as a number of standard deviations. (5 points)

6. What are Quartile 1, Quartile 2, and Quartile 3 in this data set? Use Excel to find these values. This is the only question that you must answer without using anything about the normal distribution. (5 points)

7. Is the normality assumption that was made at the beginning valid? Why or why not? Hint: Does this distribution have the properties of a normal distribution as described in the course textbook? Real data sets are never perfect, however, it should be close. One option would be to construct a histogram like you did in Project 1 to see if it has the right shape. Something in the range of 10 to 12 classes is a good number. (5 points) There are also 5 points for miscellaneous items like correct date range, correct mean, correct SD, etc. Project 3 is due by 11:59 p.m. (ET) on Monday of Module/Week 5.

PROJECT 3 INSTRUCTIONS Based on Brase & Brase: sections 6.1-6.3 Visit the NASDAQ historical prices weblink. First, set the date range to be for exactly 1 year ending on the Monday that this course started. For example, if the current term started on January 13, 2019, then use January 13, 2019 – January 12, 2020. (Do NOT use these dates. Use the dates that match up with the current term.) Do this by clicking on the blue dates after “Time Period”. Next, click the “Apply” button. Next, click the link on the right side of the page that says “Download Data” to save the file to your computer. NOTE I'M TO USE THESE DATES JAN. 13, 2019- JAN 12, 2020. PLEASE USE THESE DATES TO HELP ME ANSWER THESE QUESTIONS. I'M HAVING A DIFFICULT TIME!! This project will only use the Close values. Assume that the closing prices of the stock form a normally distributed data set. This means that you need to use Excel to find the mean and standard deviation. Then, use those numbers and the methods you learned in sections 6.1-6.3 of the course textbook for normal distributions to answer the questions. Do NOT count the number of data points. Complete this portion of the assignment within a single Excel file. Show your work or explain how you obtained each of your answers. Answers with no work and no explanation will receive no credit. 1. a) Submit a copy of your dataset along with a file that contains your answers to all of the following questions. b) What the mean and Standard Deviation (SD) of the Close column in your data set? c) If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: You do not want to calculate the mean to answer this one. The probability would be the same for any normal distribution. (5 points) 2. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at more than $1150? (5 points) 3. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $50 of the mean for that year? (between 50 below and 50 above the mean) (5 points) 4. If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than $950 per share. Would this be considered unusal? Use the definition of unusual from the course textbook that is measured as a number of standard deviations (5 points) 5. At what prices would Google have to close in order for it to be considered statistically unusual? You will have a low and high value. Use the definition of unusual from the course textbook that is measured as a number of standard deviations. (5 points) 6. What are Quartile 1, Quartile 2, and Quartile 3 in this data set? Use Excel to find these values. This is the only question that you must answer without using anything about the normal distribution. (5 points) 7. Is the normality assumption that was made at the beginning valid? Why or why not? Hint: Does this distribution have the properties of a normal distribution as described in the course textbook? Real data sets are never perfect, however, it should be close. One option would be to construct a histogram like you did in Project 1 to see if it has the right shape. Something in the range of 10 to 12 classes is a good number. (5 points) There are also 5 points for miscellaneous items like correct date range, correct mean, correct SD, etc. Project 3 is due by 11:59 p.m. (ET) on Monday of Module/Week 5.