A finance journal published a study of whether the decision to invest in the sto
ID: 3270020 • Letter: A
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 151,342 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 151,342 citizens is selected at random. Complete parts a through f.
IQ_Score
Invest_in_Market
No_Investment
Totals
1
863
4646
5509
2
1363
8649
10012
3
2149
8683
10832
4
5236
18155
23391
5
8162
24095
32257
6
10290
20183
30473
7
6301
10905
17206
8
5010
7020
12030
9
4485
5147
9632
Totals
43859
107483
151342
a.What is the probability that the Finnish citizen invests in the stock market?
(Round to the nearest thousandth as needed.)
b. What is the probability that the Finnish citizen has an IQ score of 6 or higher? (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? (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? (Round to the nearest thousandth as needed.)
e. What is the probability that the Finnish citizen does not invest in the stock market?
f. Are the events {Invest in the stock market} and {IQ score of 1} mutually exclusive?
A.Yes, they are mutually exclusive because there are no Finnish citizens who invest in the stock market and have an IQ score of 1.
B.Yes, they are mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1.
C.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.
D.No, they are not mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1.
IQ_Score
Invest_in_Market
No_Investment
Totals
1
863
4646
5509
2
1363
8649
10012
3
2149
8683
10832
4
5236
18155
23391
5
8162
24095
32257
6
10290
20183
30473
7
6301
10905
17206
8
5010
7020
12030
9
4485
5147
9632
Totals
43859
107483
151342
Explanation / Answer
a.What is the probability that the Finnish citizen invests in the stock market?
Number of Finland citizens = 151,342
Number of people invest in stock market = 43859
Probability that the Finnish citizen invests in the stock market = 43859/151342 = 0.2898
b. What is the probability that the Finnish citizen has an IQ score of 6 or higher? (Round to the nearest thousandth as needed.)
Number of Finnish citizen has an IQ score of 6 or higher = 30473 + 17206 + 12030 + 9632 = 69341
Probability that the Finnish citizen has an IQ score of 6 or higher = 69341/151342 = 0.4582
c. What is the probability that the Finnish citizen invests in the stock market and has an IQ score of 6 or higher? (Round to the nearest thousandth as needed.)
Number of Finnish citizen invests in the stock market and has an IQ score of 6 or higher = 10290 + 6301 + 5010 + 4485 = 26086
Probability that Finnish citizen invests in the stock market and has an IQ score of 6 or higher = 26086/151342 = 0.1724
d. What is the probability that the Finnish citizen invests in the stock market or has an IQ score of 6 or higher? (Round to the nearest thousandth as needed.)
Number of Finnish citizen invests in the stock market or has an IQ score of 6 or higher = Number of Finnish citizen invests in the stock market + Number of Finnish citizen who do not invests in the stock market and has an IQ score of 6 or higher
= 43859 + (20183 + 10905 + 7020 + 5147) = 87114
Probability that the Finnish citizen invests in the stock market or has an IQ score of 6 or higher = 87114/151342 = 0.5756
e. What is the probability that the Finnish citizen does not invest in the stock market?
Number of Finnish citizen does not invest in the stock market = 107483
Probability that the Finnish citizen does not invest in the stock market = 107483/151342 = 0.7102
f. Are the events {Invest in the stock market} and {IQ score of 1} mutually exclusive?
Let A be the event {Invest in the stock market} and B be the event {IQ score of 1}
If the events are mutually exclusive if P(A and B) = 0, That is, Number of Finnish citizen who invest in market and have IQ score of 1 is zero. But the Number of Finnish citizen who invest in market and have IQ score of 1 is 863 and not 0. So both events are not mutually excusive.
So, the correct answer is D.No, they are not mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.