) Annual returns on the more than 5000 common stocks available to investors vary a lot. In a recent year, the mean return was 8.3% and the standard deviation of return was 28.5%. The law of large numbers says that A. you can get an average return higher than the mean 8.3% by investing in a large number of stocks. B. as you invest in more and more stocks chosen at random that year, your average return on these stocks gets ever closer to 8.3%. C. if you invest in a large number of stocks chosen at random, your average return will have approximately a Normal distribution. D. None of the above. (b) The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
(a) Annual returns on the more than 5000 common stocks available to investors vary a lot. In a recent year, the mean return was 8.3% and the standard deviation of return was 28.5%. The law of large numbers says that
A. you can get an average return higher than the mean 8.3% by investing in a large number of stocks.
B. as you invest in more and more stocks chosen at random that year, your average return on these stocks gets ever closer to 8.3%.
C. if you invest in a large number of stocks chosen at random, your average return will have approximately a Normal distribution.
D. None of the above.
(b) The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that
A. as we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs of this type.
B. the average burnout time of a large number of bulbs has a distribution that is close to Normal.
C. the average burnout time of a large number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs.
D. None of the above.
(c) The Bureau of Labor Statistics announces that last month it interviewed all members of the labor force in a sample of 60000 households; 4.9% of the people interviewed were unemployed. The boldface number is a
A. statistic.
B. parameter.
C. sampling distribution.
D. None of the above.
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