Question

A finance journal published a study of whether the decision to invest in the stock market is dependent on IQ. Information on a sample of 155,833 adults living in Finland formed the database for the study. An IQ score​ (from a low score of 1 to a high score of​ 9) was determined for each Finnish citizen as well as whether or not the citizen invested in the stock market. The following table gives the number of Finnish citizens in each IQ​ score/investment category. Suppose one of the 155,833 citizens is selected at random. Complete parts a through f.

IQ Score	Invest in Market		No Investment		Totals
1	838		4,642		5,480
2	1,306		8,647		9,953
3	2,023		9,995		12,018
4	5,326		18,301		23,627
5	8,063		24,302		32,365
6	10,326		21,853		32,179
7	6,983		11,085		18,068
8	5,123		7,216		12,339
9	4,561		5,243		9,804
Totals	44,549		111,284		155,833

a. What is the probability that the Finnish citizen invests in the stock​ market?

The probability is _________.​(Round to the nearest thousandth as​ needed.)

b. What is the probability that the Finnish citizen has an IQ score of 6 or​ higher?

The probability is _____________ ​(Round to the nearest thousandth as​ needed.)

c. What is the probability that the Finnish citizen invests in the stock market and has an IQ score of 6 or​ higher?

The probability is __________​(Round to the nearest thousandth as​ needed.)

d. What is the probability that the Finnish citizen invests in the stock market or has an IQ score of 6 or​ higher?

The probability is ________________​(Round to the nearest thousandth as​ needed.)

e. What is the probability that the Finnish citizen does not invest in the stock​ market?

The probability is ______________​(Round to the nearest thousandth as​ needed.)

f. Are the events​ {Invest in the stock​ market} and​ {IQ score of​ 1} mutually​ exclusive?

A.​No, they are not mutually exclusive because the probability that a Finnish citizen invests in the stock market and has an IQ score of 1 is very small.

B.​No, they are not mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1.

C.​Yes, they are mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1.

D.​Yes, they are mutually exclusive because there are no Finnish citizens who invest in the stock market and have an IQ score of 1.

Answer 1

(a) No. of Finnish citizens who invests in the stock market = 44,549

Thus, the required probability is = 44,549/155,833

= 0.286

(b) No. of Finnish citizens who have an IQ score of 6 or more

= 32,179 + 18,068 + 12,339 + 9,804 = 72,390

Thus, the required probability = 72,390/155,833 = 0.465

(c) No. of Finnish citizens who invests in the stock market and has an IQ score of 6 or higher = 10,326 + 6,983 + 5,123 + 4,561

= 26,993

Thus, the required probability = 26,993/155,833 = 0.173

(d) No. of Finnish citizens who invests in the stock market or has an IQ score of 6 or higher = 44,549 + 72,390 - 26,993

= 89,946

Thus, the required probability = 89,946/155,833 = 0.577

(e) No. of Finnish citizens who do not invests in the stock market = 111,284

Thus, the required probability = 111,284/155,833 = 0.714

(f) Correct answer is option (B)