4. We know that the amount of recoverable oil in an Alaskan refuge is normally distributed witha mean of 10.850 billion barrels and a standard deviation of 2.575 billion barrels.(a) What is the probability that the actual amount of recoverable oil is less than 13 billionbarrels?(b) The projected price of the oil is $28.62 per barrel. If there needs to be a minimumof $198,000,000,000 generated to make the project feasible, then the minimum numberof barrels required to accomplish this is approximately 7 billion barrels. What is theprobability they will not reach the minimum number of barrels needed?

Answered: 4. We know that the amount of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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I2 The market portfolio has an expected return of 10% and consists of 30% in stock and 70% in real estate, and the risk-free interest rate is 5%. Based on the single-factor CAPM model and the following information on stock and property returns: The standard deviation of stock performance: 0.2 The standard deviation of real estate performance: 0.1 The correlation between stock return and real estate return: 0.3 1. What is the expected return for the stock and real estate? ** Please show detailed calculation
4. When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50 passengers that were aboard is taken. The amount they paid for the voyage and whether or not they survived is recorded. A model is fit to predict the probability they survived when the ship sank is obtained. Survived Logistic Fit of Survived By Fare 1.00 0.75 0.50- 0.25- 50 4 Parameter Estimates 100 Term Intercept -1.404254 0.4353289 Fare 0.01246686 0.0097945 For log odds of Yes/No Fare Estimate Std Error ChiSquare 10.41 1.62 150 200 Prob>ChiSq 0.0013* 0.2031 No Yes a) Suppose someone paid a fare of 25 pounds. Predict the probability they survived. b) How much would someone pay to have at least a 65% chance of survival?
Andrew plans to retire in 30 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.What is the probability that the mean return will be less than 6%?
5. For a certain disease, 40% of untreated patients can be expected to improve within a week. We observe a population of 80 untreated patients and record the percentage who improve within one week. According to the Central Limit Theorem, such percentages are approximately normally distributed. Find the mean and standard deviation of this normal distribution. Round the standard deviation to two decimal places.
An investor wants to invest $300,000 in a portfolio of three mutual funds. The annual fund returns are normally distributed with a mean of 2.00% and standard deviation of 0.30% for the short-term investment fund, a mean of 5.00% and standard deviation of 2.50% for the intermediate-term fund, and a mean of 6.25% and standard deviation of 5.50% for the long-term fund. An initial plan for the investment allocation is 45% in the short-term fund, 35% in the intermediate-term fund, and 20% in the long-term fund. a. Use Analysis ToolPak, with a seed of 1, to develop a Monte Carlo simulation with 100 trials to estimate the mean ending balance after the first year. Note: Round the final answer to two decimal places. Mean ending balance after the first year b. If the allocation is changed to 30% short-term, 55% intermediate-term, and 15% long-term, estimate the ending balance after the first year. Note: Round the final answer to two decimal places. Mean ending balance after the first year c.…
4. When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50 passengers that were aboard is taken. The amount they paid for the voyage and whether or not they survived is recorded. A model is fit to predict the probability they survived when the ship sank is obtained. Survived Logistic Fit of Survived By Fare 1.00 0.75 0.50- 0.25- 50 4 Parameter Estimates 100 Term Intercept -1.404254 0.4353289 Fare 0.01246686 0.0097945 For log odds of Yes/No Fare Estimate Std Error ChiSquare 10.41 1.62 150 200 Prob> ChiSq 0.0013 0.2031 No Yes a) Suppose someone paid a fare of 25 pounds. Predict the probability they survived. b) How much would someone pay to have at least a 65% chance of survival?
Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. What is the probability (assuming that past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 10%? What is the probability that the mean return will be less than 5%?
5. A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average. a. What is the cumulative distribution function of the time until failure? b. What is the probability that a transducer chosen at random functions for eight years without failure? irteen Reliability and Maintainability c. What is the probability that a transducer that has functioned for eight years con- tinues to function for another eight years?
1. A automobile lubrication shop keeps track of the length of time it takes to change the oil in a customer's car. From the past records they have found that the length of an oil change is normally distributed with a mean μ = 35 minutes and a standard deviation σ = 6 minutes. What is the probability that the average length of time for nine oil changes will be 40 minutes or longer?

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