SCENARIO 8-12
The Three Brothers Energy Drink Company bottles and distributes a
popular drink for athletes and exercise enthusiasts. Because of its
marketing successes the company has installed an additional filling
machine and the managers are eager to use it in daily operations.
The machine is set to fill bottles at 16 oz.
However, we know there is inherent machine variability and quality
control has determined through testing a mean of 16.2 oz. and a
standard deviation of 0.3 oz. using a 100 bottle sample.
Refer to Scenario 8-12.
Find a 90% confidence interval for the mean volume of the filled
bottle contents.
In: Economics
During a 5-week period in 2007, the stock of an insurance company and the stock of a small tech company showed the following weekly percentage changes.
| Company | Weekly Price Change (%) | ||||
| Insurance Stock | 2 | -1 | -1.7 | 0.6 | -0.3 |
| Tech Stock | 3 | 2.2 | 1.3 | -4.3 | 1.7 |
Find the variance of the weekly price changes of each. (Round your
answers to four decimal places.)
| insurance stock | ||
| tech stock |
Relate the two variances found to the riskiness of the two stocks.
The two stocks have the same riskiness.The insurance stock is riskier. No statement about the riskiness of these stocks can be made.The tech stock is riskier.
In: Statistics and Probability
The desired percentage SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility using a significance level of .01, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with σ = 0.3 and that ¯x = 5.25.
a. Does this indicate conclusively that the true average percentage differs from 5.5?
b. If the true average percentage is µ = 5.6 and a level α = .01 based on n = 16 is used, what is the probability of detecting this departure from H0?
c. What value of n is required to satisfy α = .01 and β(5.6) = .01?
In: Statistics and Probability
Consider the following scenario analysis:
| Rate of Return | |||||
| Scenario | Probability | Stocks | Bonds | ||
| Recession | 0.2 | -7 | % | 19 | % |
| Normal economy | 0.5 | 20 | 7 | ||
| Boom | 0.3 | 23 | 6 | ||
Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.
a. What is the rate of return on the portfolio in each scenario?
Rate of Return
Recession_______%
Normal economy_______%
Boom______%
b. What are the expected rate of return and standard deviation of the portfolio?
Expected return____%
Standard deviation_____%
c. Would you prefer to invest in the portfolio, in stocks only, or in bonds only? Explain the benefit of diversification.
Invest in ?
Stock only
Bond Only
Portfolio
In: Finance
Suppose that during a recent year for the United States, merchandise imports were $2.2 trillion, unilateral transfers were a net outflow of $0.2 trillion, service exports were $0.3 trillion, service imports were $0.1 trillion, and merchandise exports were $1.6 trillion.
The merchandise trade deficit was ? trillion. (Enter your response rounded to one decimal place.)
The balance on goods and services was ? trillion. (Enter your response rounded to one decimal place and include a minus sign if necessary.)
The current account balance was ? trillion. (Enter your response rounded to one decimal place and include a minus sign if necessary.)
In: Economics
The first column contains time in seconds and the second column the concentration of reactant in molar units.
| e | 0.0256 |
| 0.1 | 0.0195 |
| 0.2 | 0.0143 |
| 0.3 | 0.0105 |
| 0.45 | 0.0074 |
| 0.5 | 0.0066 |
| 0.6 | 0.0060 |
| 0.7 | 0.0031 |
| 0.8 | 0.0024 |
| 0.9 | 0.0031 |
| 1 | 0.0019 |
| 1.1 | 0.0022 |
| 1.2 | 0.0005 |
| 1.3 | 0.0012 |
| 1.4 | 0.0006 |
| 1.5 | 0.0009 |
What is the rate constant of the reaction? Be sure you include units. Use "M" for molar and "s" for seconds ?
What is the rate of the reaction at t = 0.5s? Express your answer in units of M/s
What is the concentration of product at t = 0.5s?
In: Chemistry
You are the actuary in charge of purchasing a reinsurance contract for your insurance company. You have determined that the losses that you want reinsured follow a uniform distribution on the interval [1000, 2000]. You have a choice of two reinsurance contracts for these losses. The first contract will pay 90% of the loss, while the second contract will pay up to a maximum limit, where the limit is set so that the expected payment for both contracts are the same. Find the ratio of the variance of the reinsurance payment under the second policy to the variance of the reinsurance payment under the first policy.
A. 1.5
B. 1.2
C. 0.9
D. 0.6
E. 0.3
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?
In: Finance
The weights of the native North American Blue Jay have a mean of 18.4 ounces with a standard deviation of 3.6 ounces. The distribution can be considered normal. What is the 2.5th percentile of all weights?
A. 11.344
B. 14.800
C. 13.792
D. 12.478
For the data in problem 7, what is the 97.5th percentile of all weights? A. 25.456
B. 27.688
C. 24.322
D. Can’t tell from the given data
A population of fruit flies has 30% black and 70% gray flies. If 10 flies are selected from this population, what is the probability that exactly four are black?
A. 0.2
B. 0.3
C. 0.4
D. 0.5
In: Statistics and Probability
Use the following data for questions below.
|
Week |
New Cars Sold |
|
May |
15 |
|
June |
11 |
|
July |
14 |
|
August |
17 |
|
September |
13 |
|
October |
14 |
|
November |
Using two month moving average, what is the forecast for November?
Using the three month weighted average with 0.2, 0.3, 0.5 as weights (0.5 is the weight on the most recent data), what is the forecast for November?
Using two exponential smoothing with an alpha of .4 and assuming May sales is 15, what is the forecast for November?
In: Statistics and Probability