Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
The production capacity of a production entity is normally distributed with a mean of 100 and a standard deviation of 40. Calculate the 12th percentile of the production capacity.
Below is a compact z‑table extract sufficient to answer this question directly.
Standard Normal (Z) Table – Selected Values
| z‑score | P(Z ≤ z) |
|---|---|
| −1.28 | 0.1003 |
| −1.25 | 0.1056 |
| −1.20 | 0.1151 |
| −1.17 | 0.1210 |
| −1.15 | 0.1251 |
| −1.10 | 0.1357 |
Other
Community
NNikitesh
A
50
B
56
C
53
D
54
Explanation:
Let’s walk through this carefully and intuitively.
Step 1: Understand the problem
Production capacity is normally distributed with:
- Mean (μ) = 100
- Standard deviation (σ) = 40
We are asked for the 12th percentile, meaning 12% of outcomes fall below this value.
Step 2: Convert percentile to a z‑score
In a normal distribution, percentiles are found using z‑scores.
We want:
From the provided z‑table, the closest probability to 0.12 is 0.1210, which corresponds to:
(The negative sign makes sense because the 12th percentile is below the mean.)
Step 3: Convert back to the original scale
Step 4: Evaluate answer choices
- 50 (A): Too low → corresponds to a much smaller percentile
- 56 (B): Not far enough below the mean
- 53 (C) ✅ Correct calculation
- 54 (D): Slightly higher than the true percentile
Key intuition (FRM exam tip)
Percentiles below 50% always use negative z‑scores, and the distance from the mean is driven by the standard deviation.
✅ Correct answer: C (53)
Comments
Loading comments...