Reasoning Probability Zscore
1. Problem 16 asks to determine the type of reasoning applied in the argument: "The first ball I picked from a box is green. The second ball I picked from the box is green. Therefore, all the balls in the box are green."
2. This argument observes specific cases and generalizes to all cases, which is characteristic of **Inductive Reasoning**.
3. Problem 17 asks which statement represents Deductive Reasoning given: "All cats have a keen sense of smell. Belle is a cat, _____."
4. Deductive reasoning starts from a general statement and applies it to a specific case to reach a conclusion. The correct completion is: "Therefore, Belle has a keen sense of smell."
5. Problem 14 asks about the standard deviation indicated by a tall and narrow bell-shaped curve.
6. A tall and narrow bell curve means data points are closely clustered around the mean, indicating a **smaller standard deviation**.
7. Problem 15 asks for the type of reasoning that starts from general to specific statements.
8. This is the definition of **Deductive Reasoning**.
9. Problem 12 asks to determine the area when $z = -1.31$.
10. Using standard normal distribution tables, the area to the left of $z = -1.31$ is approximately **0.0969**. However, the options given are 0.8467, 0.0369, 0.4418, 0.4049. The closest correct area for $z = -1.31$ to the left is **0.0969**, but since it's not listed, possibly the question refers to the area between $z = -1.31$ and 0, which is about 0.4049.
11. Problem 13 asks how many workers are included in the distribution if there are 1000 workers and the area between $z = -1.31$ and $z = 1.57$ is shaded.
12. The area between $z = -1.31$ and $z = 1.57$ is approximately 0.847 (or 84.7%). Therefore, the number of workers included is about $1000 \times 0.847 = 847$ workers.
13. Problem 11 asks to determine the area under the normal curve between $z = -1.31$ and $z = 1.57$.
14. The area is approximately **0.8467**.
15. Problem 10 asks for the probability rating for $z = -0.96$.
16. The area to the left of $z = -0.96$ is approximately 0.1685 or 16.85%.
17. Problem 8 asks for the standard score.
18. Without additional context, the standard score options are given; the correct standard score is likely **0.9898** based on typical z-score values.
19. Problem 9 asks which instruction corresponds to the shaded area to the right of $z = 2.32$.
20. The correct description is **"to the right of z = 2.32"**.
21. Problem 7 asks to determine the area under the curve between $z=0$ and $z=2.32$.
22. The area between $z=0$ and $z=2.32$ is approximately 0.4898.
23. Problem 3 asks to determine the Z score if $x=60$, $\bar{x}=65$, and $s=8$.
24. The formula for Z score is $$Z = \frac{x - \bar{x}}{s} = \frac{60 - 65}{8} = -0.625$$ which rounds to **-0.63**.
Final answers:
- 16: Inductive Reasoning
- 17: "Therefore, Belle has a keen sense of smell."
- 14: The value of the standard deviation is lesser.
- 15: Deductive Reasoning
- 12: 0.4049 (area between $z=-1.31$ and 0)
- 13: 847 workers
- 11: 0.8467
- 10: 16.85%
- 8: 0.9898
- 9: to the right of z = 2.32
- 7: 0.4898
- 3: -0.63