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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: Q34E (page 227)

Stock market participation and IQ. Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the stock market is dependent on IQ, Exercise 3.46 (p. 182). Recall that an IQ score (from a low score of 1 to a high score of 9) was determined for each in a sample of 158,044 Finnish citizens. Also recorded was whether or not the citizen invested in the stock market. The accompanying table gives the number of Finnish citizens in each IQ score/investment category. Which group of Finnish citizens (market investors or noninvestors) has the highest average IQ score?
IQ Score
Invest in market
No investment
Totals
1
893
4659
5552
2
1340
9409
10749
3
2009
9993
12002
4
5358
19682
25040
5
8484
24640
33124
6
10270
21673
31943
7
6698
11260
17958
8
5135
7010
12145
9
4464
5067
9531
Totals
44651
113393
158044

Short Answer

Expert verified

The highest average IQ score is 28.46 for IQ score 1.

Step by step solution

01

Given information

The table shows the citizens in each IQ score or investment category. Here, it is also recorded that the citizen are invested in the stock market.

02

Calculating highest average IQ score

IQ Score	Invest in market	No investment	Totals	Average
1	893	4659	5552	28.46
2	1340	9409	10749	14.7
3	2009	9993	12002	13.16
4	5358	19682	25040	6.31
5	8484	24640	33124	4.77
6	10270	21763	31943	4.94
7	6698	11260	17958	8.8

8	5135	7010	12145	13.01
9	4464	5067	9531	16.58

Thus, the highest average IQ is 28.46 for IQ score 1.

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Most popular questions from this chapter

4.126 Wear-out of used display panels.Wear-out failure time ofelectronic components is often assumed to have a normaldistribution. Can the normal distribution be applied to thewear-out of used manufactured products, such as coloreddisplay panels? A lot of 50 used display panels was purchasedby an outlet store. Each panel displays 12 to 18 colorcharacters. Prior to the acquisition, the panels had been usedfor about one-third of their expected lifetimes. The data inthe accompanying table (saved in the file) give the failuretimes (in years) of the 50 used panels. Use the techniquesof this section to determine whether the used panel wear-outtimes are approximately normally distributed.

0.01 1.21 1.71 2.30 2.96 0.19 1.22 1.75 2.30 2.98 0.51

1.24 1.77 2.41 3.19 0.57 1.48 1.79 2.44 3.25 0.70 1.54

1.88 2.57 3.31 0.73 1.59 1.90 2.61 1.19 0.75 1.61 1.93

2.62 3.50 0.75 1.61 2.01 2.72 3.50 1.11 1.62 2.16 2.76

3.50 1.16 1.62 2.18 2.84 3.50

Compute the following:

a. $\frac{7!}{3! (7 - 3)!}$

b. $(\begin{array}{l} 9 \\ 4 \end{array})$

c. $(\begin{array}{l} 5 \\ 0 \end{array})$

d. $(\begin{array}{l} 4 \\ 4 \end{array})$

e. $(\begin{array}{l} 5 \\ 4 \end{array})$

The random variable x has a normal distribution with $μ = 1000$ and $σ = 10$ .

a. Find the probability that x assumes a value more than 2 standard deviations from its mean. More than 3 standard deviations from . $μ$

b. Find the probability that x assumes a value within 1 standard deviation of its mean. Within 2 standard deviations of $μ$ .

c. Find the value of x that represents the 80th percentile of this distribution. The 10th percentile.

Making high-stakes insurance decisions. The Journal of Economic Psychology (September 2008) published the results of a high-stakes experiment in which subjects were asked how much they would pay for insuring a valuable painting. The painting was threatened by fire and theft, hence, the need for insurance. To make the risk realistic, the subjects were informed that if it rained on exactly 24 days in July, the painting was considered to be stolen; if it rained on exactly 23 days in August, the painting was considered to be destroyed by fire. Although the probability of these two events, “fire” and “theft,” was ambiguous for the subjects, the researchers estimated their probabilities of occurrence at .0001. Rain frequencies for the months of July and August were shown to follow a Poisson distribution with a mean of 10 days per month.

a. Find the probability that it will rain on exactly 24 days in July.

b. Find the probability that it will rain on exactly 23 days in August.

c. Are the probabilities, parts a and b, good approximations to the probabilities of “fire” and “theft”?

Public transit deaths. Millions of suburban commuters use the public transit system (e.g., subway trains) as an alter native to the automobile. While generally perceived as a safe mode of transportation, the average number of deaths per week due to public transit accidents is 5 (Bureau of Transportation Statistics, 2015).

a. Construct arguments both for and against the use of the Poisson distribution to characterize the number of deaths per week due to public transit accidents.

b. For the remainder of this exercise, assume the Poisson distribution is an adequate approximation for x, the number of deaths per week due to public transit accidents. Find $E (x)$ and the standard deviation of x.

c. Based strictly on your answers to part b, is it likely that more than 12 deaths occur next week? Explain.

d. Find $p (x > 12)$ . Is this probability consistent with your answer to part c? Explain.

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