Probability · univariate distributions diagnostic PDF
Exam P Univariate Distributions: 30 Worked Problems
Practice model selection, parameter conventions, moments, quantiles, transformations, and insurance-payment variables across the univariate syllabus.
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- New practice problems
- 30
- Pages
- 76
- Time limit
- 180 min
- Price
- $19
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One original Exam P practice question with full solution
A quality score takes values 1, 3, 5, 7, and 9 with probabilities 0.10, 0.20, 0.40, 0.20, and 0.10. What probability lies within one standard deviation of its mean, including endpoints?
- 0.20
- 0.40
- 0.60
- 0.80
- 1.00
Symmetry gives mean 5 and variance 4.8, so the interval is about [2.81,7.19]. Scores 3, 5, and 7 contribute probability 0.80.
Setup
Use symmetry of the five-point score distribution to obtain mean 5, then compute its variance from squared deviations about 5.
Model
The variance is 4.8, giving standard deviation 2.1909 and interval [2.8091,7.1909].
Compute
Only scores 3, 5, and 7 lie in the interval. Their probabilities sum to 0.20+0.40+0.20=0.80.
Answer
Hence the required probability is 0.80, corresponding to choice D.
Why the other choices are wrong
- A
- The value 0.20 counts only one of the two symmetric neighboring scores and omits both the center and the other neighbor.
- B
- The value 0.40 is the mass at score 5 alone; scores 3 and 7 also lie within one standard deviation.
- C
- The value 0.60 includes the center and only one of the two symmetric neighboring scores.
- E
- The value 1.00 includes scores 1 and 9, each four units from the mean and therefore outside the radius 2.1909.
Independent answer check
| Primary value | 0.8 |
|---|---|
| Primary method | Compute the variant by direct discrete moment calculation and support filtering. |
| Independent value | 0.8 |
| Independent method | Computing each absolute deviation from 5 directly includes 3 and 7 but excludes 1 and 9, giving 0.80. |
| Answer | D · agreement passed |
Contents
Inside the 76-page edition
Candidates preparing in English for the Probability (P) Exam
Table of contents
- 30 original univariate problems
- Discrete and continuous model selection
- Moments, percentiles, and transformations
- Deductibles and payment variables
- 120 wrong-choice analyses and two-path checks
What is included
30 verified original variants selected without duplication for this focused diagnostic. Official problem wording is not included.
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Every included result is reproducible
Every selected problem already passed a reproducible calculation, an independent second method, and answer-letter agreement. The compiler rejects any failed check, cross-product duplicate, or official source wording.
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Questions about this edition
Are these official sample questions?
No. Every question is an independently written original variant. Official problem wording is not reproduced.
Are complete solutions included?
Yes. Every problem includes Setup, Model, Compute, and Answer steps plus a concrete explanation for each of the four incorrect choices.
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Does this overlap the complete proof manual?
Yes. These 30 original variants are selected from the verified variant bank included in the Probability Proof Manual. This edition adds a curated focused diagnostic, answer sheet, answer key, and focused purchase price.
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Probability Univariate Distributions Practice Workbook
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