How long will it take for an initial deposit of $2,500 to grow to be $4,000, if the interest rate is 5% per year, compounded annually?
Answer(s): B
Either the $2,500 or the $4,000 must be entered as a negative number - it won't matter which. On the BAII Plus, press 5 I/Y, 2500 PV, 0 PMT, 4000 +/- FV, CPT N. On the HP12C, press 5 i, 2500 PV, 0 PMT, 4000 CHS FV,F. Note that the HP12C will indicate 10 years for the answer.
Which of the following is/are true?
Answer(s): C
Adding a constant changes the mean by the same amount and leaves the variance and standard deviation unchanged. Multiplying with a constant causes the mean and the standard deviation to be multiplied by the same constant. The variance gets multiplied by the square of the constant.
If the alternate hypothesis states that u (Mu) does not equal 4,000, what is the rejection region for the hypothesis test?
Answer(s): E
The alternate hypothesis says does not equal, which means it could be less or more than 4000. So we must consider both tails.
An investor faces the following investment scenarios:Scenario Probability ReturnBull market 60% 30%Neutral market 30% 7%Market crash 10% -25%The variance of the investor's rate of return is ________.
The expected return equals 0.6 * 30% + 0.3 * 7% + 0.1*(-25%) = 17.6%. To calculate the variance, an easy way is to first calculate the second moment, which is the expected value of the square of the return. Thus, the second moment equals 0.6*[(30%)^2] + 0.3*[(7%)^2)] + 0.1*[(-25%)^2] = 617.2%%.The variance of a random variable equals the second moment minus the square of the mean. In this case, the variance equals 617.2%% - 17.6%^2 = 307.4%%
According to Chebyshev's Theorem, what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?
Answer(s): D
Chebyshev's theorem applies regardless of the shape of the distribution. The minimum proportion that lie within k standard deviations of the mean is at least 1-[1/(k^2)]. In this case k = 1.75. k^2 = 3.0625. So we get 67%.
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