Chapter 4: Q10. (page 217)
Stock market. Give an example of a continuous random variable that would be of interest to a stockbroker.
Example: The time taken by a stockbroker for the completion of the transactions of the stocks.
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Suppose xis a binomial random variable with n= 20 and
p= .7.
a. Find.
b. Find.
c. Find.
d. Find.
e. Find.
f. Find,, and.
g. What is the probability that xis in the interval?
How many questionnaires to mail? The probability that a consumer responds to a marketing department’s mailed questionnaire is 0.4. How many questionnaires should be mailed if you want to be reasonably certain that at least 100 will be returned?
4.131 Chemical composition of gold artifacts. The Journal of Open Archaeology Data(Vol. 1, 2012) provided data onthe chemical composition of more than 200 pre-Columbiangold and gold-alloy artifacts recovered in the archaeologicalregion inhabited by the Muisca of Colombia (a.d.600–1800). One of many variables measured was the percentageof copper present in the gold artifacts. Summary statisticsfor this variable follow: mean = 29.94%, median = 19.75%,standard deviation = 28.37%. Demonstrate why the probabilitydistribution for the percentage of copper in thesegold artifacts cannot be normally distributed.
Suppose x is a binomial random variable with p = .4 and n = 25.
a. Would it be appropriate to approximate the probability distribution of x with a normal distribution? Explain.
b. Assuming that a normal distribution provides an adequate approximation to the distribution of x, what are the mean and variance of the approximating normal distribution?
c. Use Table I in Appendix D to find the exact value of .
d. Use the normal approximation to find .
Types of finance random variables. Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are discrete and which are continuous random variables?
a. The closing price of a particular stock on the New York Stock Exchange.
b. The number of shares of a particular stock that are traded each business day.
c. The quarterly earnings of a particular firm.
d. The percentage change in earnings between last year and this year for a particular firm.
e. The number of new products introduced per year by a firm.
f. The time until a pharmaceutical company gains approval from the U.S. Food and Drug Administration to market a new drug.
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