A bell-shaped, symmetrical frequency distribution has a mean of 50. If 68% of the observations in the distribution fall between 40 and 60, what's the range within which 99% of the observations in the distribution fall?
Answer(s): D
For a bell-shaped, symmetrical frequency distribution, approximately 68% of the observations lie within one standard deviation of the mean. The mean equals (40 + 60)/2 = 50. Therefore, the standard deviation equals 50- 40 = 10. Now, by the normal rule, 99% of the observations lie within 2.58 standard deviations of the mean.Hence, the requisite range equals [50 - 2.58*10, 50 + 2.58*10] = [24.2, 75.8].
The significance level of a test is usually equal to which of the following:
Answer(s): B
The standard method of hypothesis testing involves stating the significance level as equal to the probability of incorrectly rejecting the null hypothesis. This action is defined as a Type I error. The converse of a Type I error, in which the null hypothesis is incorrectly rejected, is a Type II error, in which a false null hypothesis is mistakenly accepted.
The first card selected from a standard 52 card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection?
There are still 4 kings out of 52 in the pack. So 4/52 = 1/13. The first selection does not affect the second selection.
If your discount rate is 8% per year, calculate the present value of the following cash flows:End of year 1: $2,200End of year 2: $3,000End of year 3: $7,300
The present value = 2,200/1.08 + 3,000/(1.08^2) + 7,300/(1.08^3) = 10,404
A firm's treasurer estimates that the firm will need about $15 million in 3 years' time to allow the acquisition of a growing software firm. If the firm can invest in the capital market at the risk-free rate of7% per year and wants to make sure it has the necessary funds available in 3 years, how much does it need to invest today?
Answer(s): A
The amount needed today equals 15/(1.07^3) = $12.244 million
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