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
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
An expensive watch is powered by a 3-volt lithium battery expected to last three years. Suppose the life of the battery has a standard deviation of 0.3 year and is normally distributed.a. Determine the probability that the watch's battery will last longer than 3.8 years.b. Calculate the probability that the watch's battery will last more than 2.15 years.c. Compute the length-of-life value for which 15% of the watch's batteries last longer.
a. The probability that the battery will last longer than 3.8 years is
b. The probability that the battery will last more than 2.15 years is
c. The length-of-life value for which 15% of the batteries last longer is years.
In: Statistics and Probability
A peanut can has the usual “can shape” of a circular cylinder. Its sides are made of cardboard, its bottom is made of thick plastic-coated aluminum foil, and its top lid is made of clear plastic. It must have a volume of 480 cubic centimeters. The cardboard material used for the sides costs 0.1 cents per square centimeter, the foil material used for the bottom costs 0.3 cents per square centimeter, and the plastic material used for the top lid costs 0.5 cents per square centimeter. What dimensions should the can have in order to minimize the cost of the materials from which it is made?
In: Math
Consider an annuity for 10 years, whose payments vary in geometric progression. An annual effective interest rate of 6% is used. Obtain the financial value at t = 29/05/2010 of this annuity considering different cases:
In: Accounting
A peanut can has the usual “can shape” of a circular cylinder. Its sides are made of cardboard, its bottom is made of thick plastic-coated aluminum foil, and its top lid is made of clear plastic. It must have a volume of 480 cubic centimeters. The cardboard material used for the sides costs 0.1 cents per square centimeter, the foil material used for the bottom costs 0.3 cents per square centimeter, and the plastic material used for the top lid costs 0.5 cents per square centimeter. What dimensions should the can have in order to minimize the cost of the materials from which it is made?
In: Math
A block of mass m begins at rest at the top of a ramp at elevation h with whatever PE is associated with that height. The block slides down the ramp over a distance d until it reaches the bottom of the ramp. How much of its original total energy (in J) survives as KE when it reaches the ground? (In other words, the acceleration is not zero like it was in lab and friction does not remove 100% of the original PE. How much of that original energy is left over after the friction does work to remove some?) m = 8.5 kg h = 5.5 m d = 5 m μ = 0.3 θ = 36.87°
In: Physics
Year Percentage
2000 28
2001 32
2002 36
2003 40
2004 44
2005 51
2006 53
2007 57
2008 60
2009 66
Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment.
alpha= 0.3 and beta= 0.4. Then calculate MAD.
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Quarter Price
Q1 2017 186.3
Q2 2017 190.9
Q3 2017 195.2
Q4 2017 195.2
Q1 2018 198.7
Q2 2018 201.2
Forecast the price index for Q3 2018 using a three-period simple moving average. Then calculate MAD.
In: Statistics and Probability
Two companies, ABC and XYZ, are considering entering into a
swap. Company ABC can
borrow at a fixed rate of 8.1% or, alternatively LIBOP + 1.3%.
Company XYZ faces a fixed rate of
7.5% and a floating rate of LIBOR + 0.3%.
a) Suppose that company ABC wants a floating rate loan, while
company XYZ wants a
fixed rate loan. Is there a basis for a swap? If so, set up the
swap under the assumption
that interest rate savings is split evenly by the firms.
b) Answer the same question under the assumption that company XYZ
wants a floating
rate loan, while company ABC wants a fixed rate loan.
In: Finance
A portfolio of $ 100,000 is composed of two assets: A stock whose expected annual return is 10% with an annual standard deviation of 20%; A bond whose expected annual return is 5% with an annual standard deviation of 12%. The coefficient of correlation between their returns is 0.3. An investor puts 60% in the stock and 40% in bonds.
What is the expected annual return, standard deviation of the portfolio
What is the 1-year 95% VaR? Explain in non-technical terms the meaning of the number you calculated.
What is the 1-year 99% VaR? Explain in non-technical terms the meaning of the number you calculated
Discuss the weaknesses of Value-at-Risk as a measure of risk.
In: Finance