Question

1. the data set represents the income levels of the members of a country club. find the probability that a randomly selected member earns at least $77,000. round your answers to the nearest tenth. 93,000 109,000 75,000 117,000 76,000 93,000 77,000 73,000 133,000 173,000 74,000 85,000 125,000 76,000 109,000 101,000 77,000 141,000 72,000 101,000 a) 0.7 b) 0.6 c) 0.8 d) 0.4

Explanation:

Step1: Count total number of data points

We first find the total number of members (data points). Let's count the numbers:
First row: 10 numbers, second row: 10 numbers. So total \( n = 10 + 10=20 \).

Step2: Count numbers ≥ 77,000

Now we identify the numbers that are at least 77,000 (i.e., greater than or equal to 77,000):
93,000, 109,000, 117,000, 93,000, 77,000, 133,000, 173,000, 85,000, 125,000, 109,000, 101,000, 77,000, 141,000, 101,000. Wait, let's count again carefully:
First row: 93,000 (yes), 109,000 (yes), 75,000 (no), 117,000 (yes), 76,000 (no), 93,000 (yes), 77,000 (yes), 73,000 (no), 133,000 (yes), 173,000 (yes) → that's 8 numbers.
Second row: 74,000 (no), 85,000 (yes), 125,000 (yes), 76,000 (no), 109,000 (yes), 101,000 (yes), 77,000 (yes), 141,000 (yes), 72,000 (no), 101,000 (yes) → that's 8 numbers? Wait no, let's list all:
From first row (10 elements):
- 93,000: ≥77k ✔️
- 109,000: ≥77k ✔️
- 75,000: <77k ❌
- 117,000: ≥77k ✔️
- 76,000: <77k ❌
- 93,000: ≥77k ✔️
- 77,000: ≥77k ✔️
- 73,000: <77k ❌
- 133,000: ≥77k ✔️
- 173,000: ≥77k ✔️
So first row: 8 elements (wait 93,000 (1), 109,000 (2), 117,000 (3), 93,000 (4), 77,000 (5), 133,000 (6), 173,000 (7) → wait no, I miscounted. Let's do it one by one:
1. 93,000: yes (1)
2. 109,000: yes (2)
3. 75,000: no
4. 117,000: yes (3)
5. 76,000: no
6. 93,000: yes (4)
7. 77,000: yes (5)
8. 73,000: no
9. 133,000: yes (6)
10. 173,000: yes (7)
So first row: 7 yes.
Second row (10 elements):
1. 74,000: no
2. 85,000: yes (8)
3. 125,000: yes (9)
4. 76,000: no
5. 109,000: yes (10)
6. 101,000: yes (11)
7. 77,000: yes (12)
8. 141,000: yes (13)
9. 72,000: no
10. 101,000: yes (14)
Wait, this is wrong. Wait total data points: 20. Let's list all 20 numbers:

1. 93,000
2. 109,000
3. 75,000
4. 117,000
5. 76,000
6. 93,000
7. 77,000
8. 73,000
9. 133,000
10. 173,000
11. 74,000
12. 85,000
13. 125,000
14. 76,000
15. 109,000
16. 101,000
17. 77,000
18. 141,000
19. 72,000
20. 101,000

Now mark which are ≥77,000:

1. 93,000: yes
2. 109,000: yes
3. 75,000: no
4. 117,000: yes
5. 76,000: no
6. 93,000: yes
7. 77,000: yes
8. 73,000: no
9. 133,000: yes
10. 173,000: yes
11. 74,000: no
12. 85,000: yes (85k ≥77k: yes)
13. 125,000: yes
14. 76,000: no
15. 109,000: yes
16. 101,000: yes (101k ≥77k: yes)
17. 77,000: yes
18. 141,000: yes
19. 72,000: no
20. 101,000: yes

Now count the "yes" ones:

1. yes
2. yes
4. yes
6. yes
7. yes
9. yes
10. yes
12. yes
13. yes
15. yes
16. yes
17. yes
18. yes
20. yes

Wait let's count:

1. 93k: 1
2. 109k: 2
4. 117k: 3
6. 93k: 4
7. 77k: 5
9. 133k: 6
10. 173k: 7
12. 85k: 8
13. 125k: 9
15. 109k: 10
16. 101k: 11
17. 77k: 12
18. 141k: 13
20. 101k: 14

Wait that's 14? Wait no, let's check each:

1. 93,000: ≥77k ✔️ (1)
2. 109,000: ≥77k ✔️ (2)
3. 75,000: ❌
4. 117,000: ≥77k ✔️ (3)
5. 76,000: ❌
6. 93,000: ≥77k ✔️ (4)
7. 77,000: ≥77k ✔️ (5)
8. 73,000: ❌
9. 133,000: ≥77k ✔️ (6)
10. 173,000: ≥77k ✔️ (7)
11. 74,000: ❌
12. 85,000: ≥77k ✔️ (8)
13. 125,000: ≥77k ✔️ (9)
14. 76,000: ❌
15. 109,000: ≥77k ✔️ (10)
16. 101,000: ≥77k ✔️ (11)
17. 77,000: ≥77k ✔️ (12)
18. 141,000: ≥77k ✔️ (13)
19. 72,000: ❌
20. 101,000: ≥77k ✔️ (14)

Wait, but 20 total data points. Wait maybe I made a mistake. Wait 85,000 is ≥77,000: yes. 101,000: yes. 77,000: yes. Let's count again:

Numbers ≥77,000:

93,000 (1)

109,000 (2)

117,000 (3)

93,000 (4)

77,000 (5)

133,000 (6)

173,000 (7)

85,000 (8)

125,000 (9)

109,000 (10)

101,000 (11)

77,000 (12)

141,000 (13)

101,000 (14)

Wait that's 14? But 20 total. Wait maybe the original data is 20 numbers? Wait first row: 10, second row:10, total 20. Wait 14 out of 20? But 14/20 = 0.7. Wait the options have 0.7 as option A. Wait maybe my counting is wrong. Wait let's list all numbers and mark:

1. 93k: yes
2. 109k: yes
3. 75k: no
4. 117k: yes
5. 76k: no
6. 93k: yes
7. 77k: yes
8. 73k: no
9. 133k: yes
10. 173k: yes
11. 74k: no
12. 85k: yes
13. 125k: yes
14. 76k: no
15. 109k: yes
16. 101k: yes
17. 77k: yes
18. 141k: yes
19. 72k: no
20. 101k: yes

Now count the "yes" marks: 1,2,4,6,7,9,10,12,13,15,16,17,18,20. That's 14. 14 divided by 20 is 0.7. So the probability is 14/20 = 0.7.

Step3: Calculate probability

Probability \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \)

Number of favorable (≥77,000) = 14, Total =20.

\( P = \frac{14}{20} = 0.7 \)

Answer:

A) 0.7