A sample of assistant professors on the business faculty at state supported institutions in Ohio revealed the mean income to be $32,000 for 9 months with a standard deviation of $3,000. Using Chebyshev's Theorem, what is the proportion of faculty that earn more than $26,000 but less than $38,000?
Answer(s): C
26,000 and 38,000 are two standard deviations away from the mean. Using 1-(1/k^2) where k = 2, we get 0.75
If you deposit $7,000 into an account paying 6% per year, compounded annually, how much do you have in the account in 20 years?
Answer(s): E
On the BAII Plus, press 20 N, 6 I/Y, 7000 PV, 0 PMT, CPT FV. On the HP12C, press 20 n, 6 i, 7000 PV, 0 PMT, FV. Note that the answer will be displayed as a negative number. Make sure that the BAII Plus has the P/ Y value set to 1.
With a discount rate of 12% per year, the value of a perpetuity that pays $500 every year is:
The value of the perpetuity = 500/0.12 = 4,167
David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one hour period twenty-five customers buy gasoline at this station. What is the probability that no more than twenty pay in cash?
P(20) is almost zero. Probabilities of higher than 20 are also close to zero. So the probability of not more than 20 is almost 1.
You have invested in a stock with a expected return of 14% and a standard deviation of 7%. Your target rate of return is 7%. What is the probability that you will not meet your objective, assuming stock returns are normally distributed?
There is a 68% chance that the stock returns will be within one standard deviation of the mean i.e. with 68% chance, the stock returns will be between 7% and 21%. Hence, the probability that stock returnswill lie outside this range is 100% - 68% = 32%. Since the normal distribution is symmetrically distributed about the mean, the probability that the returns will be less than 7% equals 32/2 = 16% Instead of the above, you could also solve the problem using the z-score and the normal probability distribution table. You should, however, be aware of short-cuts like the above.
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