Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.
In: Math
Assume that engineers at a national research laboratory built a prototype automobile that could be driven 50 miles on a single gallon of water as fuel. They estimate that in mass production the car would cost $100,000 per unit to build. The engineers argue that Congress should force U.S. automakers to build this energy-efficient car. In your opinion, is energy efficiency the same thing as economic efficiency? Please explain your opinion and state whether you support it or not.
Please answer question in one paragraph.
In: Economics
|
Suppose in an asymmetric and continuous distribution P(X< -131) = P(-131<X< -57) = P(-57 < X< 29) = P(X>29). Which of the following is correct? A. mean=median=-131 B. mean=median= -57 C. median is -131, mean is unknown D. median is -57, mean is unknown E. median is -34, mean is unknown
|
|
|
In Questions 2-4 suppose there are a total of 15 Carbon Monoxide Detectors in a building and event “Y” is defined as Y={At least 9 of these detectors work}. Further suppose P(each detector work)=0.8, and detectors are independent of each other. Which of the following is the Ybar (complement of Y)? A. Ybar={At least 5 detectors fail} B. Ybar={At least 6 detectors fail} C. Ybar={At most 6 detectors fail} D. Ybar={At least 7 detectors fail} E. Ybar={At most 7 detectors fail} |
|
|
What is the probability that detectors number 3, 4, 11, 15 fail and the other 11 detectors work? A. 0.8^4 * 0.2^11 * 15!/(4! * 11!) B. 0.8^4 * 0.2^11 C. 0.8^11 * 0.2^4 * 15!/(4! * 11!) D. 0.8^11 * 0.2^4
|
|
|
What is the probability that 11 detectors work and 4 detectors fail? (Hint: Here we don’t care which 4 to fail, just any 4). A. 0.8^4 * 0.2^11 * 15!/(4! * 11!) B. 0.8^4 * 0.2^11 C. 0.8^11 * 0.2^4 * 15!/(4! * 11!) D. 0.8^11 * 0.2^4
|
In: Statistics and Probability
7. The following data is the weight of diamond x with the US dollar price y.
x : 0.3 0.4 0.5 0.5 1.0 0.7
y : 510 1151 1343 1410 5669 2277
(a) Find the regression equation for the data points given.
(b) Determine the percentage of variation in price of diamond y that is explained by the weight x.
(c) Is it reasonable to predict the price of a 0.8-carat diamond using this model? If yes, predict it. If no, state why.
(d) Is it reasonable to predict the price of a 1.5-carat diamond using this model? If yes, predict it. If no, state why.
This is strictly to check answers.
In: Statistics and Probability
Q1. A portfolio is invested 39% in Stock A, 24% in Stock B, and the remainder in Stock C. The returns for Stock A, B, and C are 11.7%, 39.2%, and 14.3% respectively. What is the portfolio's return?
Q2.
Calculate the portfolio beta based on the following information:
| Stock | Invested Amount | beta |
| A |
$2475 |
0.7 |
| B | $2159 | 0.3 |
| C | $441 | 0.8 |
Q3. The risk-free rate is 2.1%, the market risk premium = (
E(Rm) - Rf) is 6.2%, and the stock’s beta is 1.1. What is the
required rate of return on the stock, E(Ri)?
Use the CAPM equation.
i need this asap
In: Finance
| Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution. |
Table 1: X P(X) Table 2: X P(X) Table 3: X P(X)
25 0.1 25 -0.6 25 0.5
50 0.7 50 0.2 50 0.3
75 0.2 15 0.1 75 0.1
100 0.4 100 0.1 100 0.1
|
a. Which of the above tables is a probability distribution? b.Using the correct probability distribution, find the probability that x is 1. Exactly 75 = 2. No more than 50= 3. More than 25= c) Compute the mean, variance, and standard deviation of this distribution 1. Mean = 2. Variance= 3. Standard deviation = |
In: Statistics and Probability
Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.
| Actual Return | Actual Weight | Benchmark Weight | Index Return | |||||||||
| Equity | 2 | % | 0.5 | 0.4 | 2.5% (S&P 500) | |||||||
| Bonds | 1.8 | 0.3 | 0.4 | 2 (Barclay’s Aggregate) | ||||||||
| Cash | 0.6 | 0.2 | 0.2 | 0.7 | ||||||||
a-1. What was the manager’s return in the month?
a-2. What was her overperformance or underperformance?
b. What was the contribution of security selection to relative performance?
c. What was the contribution of asset allocation to relative performance?
In: Finance
Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow:
| Proportion of Services Used by | |||||||||||
| Department | Direct Costs | Maintenance | Cafeteria | Machining | Assembly | ||||||
| Machining | $ | 120,000 | |||||||||
| Assembly | 84,000 | ||||||||||
| Maintenance | 55,000 | — | 0.2 | 0.5 | 0.3 | ||||||
| Cafeteria | 42,000 | 0.7 | — | 0.2 | 0.1 | ||||||
Required:
Use the reciprocal method to allocate the service costs. (Matrix algebra is not required.) (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your final answers to the nearest whole dollar amounts.)
| Maintenance | Personnel | Printing | Developing | |
| Service department costs | ||||
| Maintenance | ||||
| Personnel | ||||
| Total | $0 | $0 | $0 | $0 |
In: Accounting
Consider the following Markov chain:
|
0 |
1 |
2 |
3 |
|
|
0 |
0.3 |
0.5 |
0 |
0.2 |
|
1 |
0.5 |
0.2 |
0.2 |
0.1 |
|
2 |
0.2 |
0.3 |
0.4 |
0.1 |
|
3 |
0.1 |
0.2 |
0.4 |
0.3 |
In: Statistics and Probability
In: Math