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Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset Vaia Explanations$ Math

13th Edition · 888 pages

ISBN: 9780134506593

Chapter 4: Q10. (page 217)

Stock market. Give an example of a continuous random variable that would be of interest to a stockbroker.

Short Answer

Expert verified

Example: The time taken by a stockbroker for the completion of the transactions of the stocks.

Step by step solution

01

Elucidating the continuous random variables

The continuous random variables are those variables that take infinite values for which it is very difficult to count by anyone. The values of continuous random variables can fluctuate a lot.

02

Specifying the example of the continuous random variables

The time taken for the completion of the transaction of stocks between two market participants through a stockbroker varies a lot. The variation in time depends upon the situation and the momentum of change in the stock prices, which means that it can take infinite values.

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Most popular questions from this chapter

Choosing portable grill displays. Refer to the Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, Exercise 3.109 (p. 204). Recall that each of 124 college students selected showroom displays for portable grills. Five different displays (representing five different-sized grills) were available. Still, the students were instructed to select only three displays to maximize purchases of Grill #2 (a smaller-sized grill). The table shows the grill display combinations and the number of times each was selected by the 124 students. Suppose one of the 124 students is selected at random. Let x represent the sum of the grill numbers selected by this student. (This value indicates the size of the grills selected.)

a. Find the probability distribution for x.

b. What is the probability that x exceeds 10?

Tracking missiles with satellite imagery.The Space-BasedInfrared System (SBIRS) uses satellite imagery to detect andtrack missiles (Chance, Summer 2005). The probability thatan intruding object (e.g., a missile) will be detected on aflight track by SBIRS is .8. Consider a sample of 20 simulated tracks, each with an intruding object. Let x equal the numberof these tracks where SBIRS detects the object.

a. Demonstrate that x is (approximately) a binomial randomvariable.

b. Give the values of p and n for the binomial distribution.

c. Find $P (x = 15)$ , the probability that SBIRS will detect the object on exactly 15 tracks.

d. Find $P (x \geq 15)$ , the probability that SBIRS will detect the object on at least 15 tracks.

e. Find $E (x)$ and interpret the result.

Identify the type of random variable—binomial, Poisson or hypergeometric—described by each of the following probability distributions:

a. $p (x) = \frac{5^{x} e^{- 5}}{x!}; x = 0, 1, 2, . . .$

b. $p (x) = (\begin{matrix} 6 \\ x \end{matrix}) {(. 2)}^{x} {(. 8)}^{6 - x}; x = 0, 1, 2, . . ., 6$

c. $p (x) = \frac{10!}{x! (10 - x)!} {(. 9)}^{x} {(. 1)}^{10 - x} : x = 0, 1, 2, . . ., 10$

185 Software file updates. Software configuration management was used to monitor a software engineering team’s performance at Motorola, Inc. (Software Quality Professional, Nov. 2004). One of the variables of interest was the number of updates to a file that was changed because of a problem report. Summary statistics for $n = 421$ n = 421 files yielded the following results: role="math" localid="1658219642985" $\bar{x} = 4 .71$ , $s = 6 .09$ , $Q_{L} = 1$ , and $Q_{U} = 6$ . Are these data approximately normally distributed? Explain.

Find each of the following probabilities for the standard normal random variable z:

$a . P (- \leq z \leq 1) b . P (- 1.96 \leq z \leq 1.96) c . P (- 1645 \leq z \leq 1.645) d . P (- 2 \leq z \leq 2)$

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