A finance journal published a study of whether the decision to invest in the sto
ID: 3056872 • 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 151,314 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 151,314 citizens is selected at random. Complete parts a through f.
IQ Score
Invest in Market
No Investment
Totals
1
848
4,698
5,546
2
1,387
8,947
10,334
3
2,011
9,461
11,472
4
5,224
18,016
23,240
5
8,149
23,168
31,317
6
10,028
20,409
30,437
7
6,069
11,314
17,383
8
5,365
6,858
12,223
9
4,478
4,884
29,362
Totals
43,559
107,755
151,314
.
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. Yes, they are mutually exclusive because there are no Finnish citizens who invest in the stock market and have an IQ score of 1.
C. No, they are not 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 Finnish citizens who invest in the stock market and have an IQ score of 1.
IQ Score
Invest in Market
No Investment
Totals
1
848
4,698
5,546
2
1,387
8,947
10,334
3
2,011
9,461
11,472
4
5,224
18,016
23,240
5
8,149
23,168
31,317
6
10,028
20,409
30,437
7
6,069
11,314
17,383
8
5,365
6,858
12,223
9
4,478
4,884
29,362
Totals
43,559
107,755
151,314
Explanation / Answer
a)probability that the Finnish citizen invests in the stock market =43559/151314 =0.288
b) probability that the Finnish citizen has an IQ score of 6 or higher =69405/151314 =0.459
c) probability that the Finnish citizen invests in the stock market and has an IQ score of 6 or higher
=(10028+6069+5365+4478)/151314=0.171
d)probability that the Finnish citizen invests in the stock market or has an IQ score of 6 or higher
=0.288+0.459-0.171 =0.575
e) probability that the Finnish citizen does not invest in the stock market =107755/151314 =0.712
f)
option C is correct
C. No, they are not mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1.
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