Problem Analysis #35

GPT-5.2 (high) · Run 1

7.11s
3,014 toks
Problem Statement

A population is normally distributed with mean mm and standard deviation 55. From this population, a random sample of size 3636 is taken, and a 99%99\% confidence interval for the population mean mm is constructed using the sample mean. The resulting confidence interval is 1.2≤m≤a1.2 \leq m \leq a. Find the value of aa. (Here, ZZ denotes a standard normal random variable, and use P(∣Z∣≤2.58)=0.99\text{P}(|Z| \leq 2.58) = 0.99.) [3 points]Compute 10a10a.\

Ground Truth
55
Execution Trace
Reasoning Process

[THOUGHT] For a 99% z-interval with known population standard deviation, the confidence interval is

xˉ±z0.995⋅σn.\bar x \pm z_{0.995}\cdot \frac{\sigma}{\sqrt{n}}.

Given the lower endpoint is 1.2, we have xˉ−ME=1.2\bar x - \text{ME}=1.2, so xˉ=1.2+ME\bar x=1.2+\text{ME}. Then the upper endpoint is a=xˉ+ME=1.2+2MEa=\bar x+\text{ME}=1.2+2\text{ME}. I will compute ME=2.58⋅5/36\text{ME}=2.58\cdot 5/\sqrt{36} and then 10a10a. [/THOUGHT] [PYTHON] import math sigma = 5 n = 36 z = 2.58 ME = z * sigma / math.sqrt(n) a = 1.2 + 2ME print("ME =", ME) print("a =", a) print("10a =", 10a) [/PYTHON][THOUGHT] For a 99% z-interval with known population standard deviation, the confidence interval is

xˉ±z0.995⋅σn.\bar x \pm z_{0.995}\cdot \frac{\sigma}{\sqrt{n}}.

Given the lower endpoint is 1.2, we have xˉ−ME=1.2\bar x - \text{ME}=1.2, so xˉ=1.2+ME\bar x=1.2+\text{ME}. Then the upper endpoint is a=xˉ+ME=1.2+2MEa=\bar x+\text{ME}=1.2+2\text{ME}. I will compute ME=2.58⋅5/36\text{ME}=2.58\cdot 5/\sqrt{36} and then 10a10a. [/THOUGHT] [PYTHON] import math sigma = 5 n = 36 z = 2.58 ME = z * sigma / math.sqrt(n) a = 1.2 + 2ME print("ME =", ME) print("a =", a) print("10a =", 10a) [/PYTHON]

Tool Output
[PYTHON OUTPUT] ME = 2.15 a = 5.5 10a = 55.0 [/PYTHON OUTPUT] [PYTHON OUTPUT] ME = 2.15 a = 5.5 10a = 55.0 [/PYTHON OUTPUT]
Reasoning Process

[THOUGHT] Using the computed margin of error 2.152.15, the upper endpoint is a=5.5a=5.5, so 10a=5510a=55. 55\boxed{55}

Final Model Output
55

Comparative Analysis (P35) (Average across runs)

Avg Time Taken

EXAONE-4.0.1-32B (high)
636.4
K-EXAONE-236B-A23B
109.6
Llama-VARCO-8B-Instruct
80.1
HCX-007(high)
49.6
Deepseek-V3.2
47.8
Kanana-2-30B-Thinking
46.1
Gemini-3-Pro-Preview
24.4
Kanana-2-30B-Thinking-2601
22.1
Solar-Pro-2 (31B)(high)
16.4
Solar-Open-100B
14.7
Claude-Opus-4.5
13.8
A.X-4.0 (72B)
13.8
Grok-4.1-fast
10.6
GPT-5.1 (high)
7.8
GPT-5.2 (high)
7.1
K-EXAONE-236B-A23B
6.3

Avg Token Usage

K-EXAONE-236B-A23B
12,259
Kanana-2-30B-Thinking
9,114
Kanana-2-30B-Thinking-2601
6,664
Llama-VARCO-8B-Instruct
6,041
HCX-007(high)
5,122
Gemini-3-Pro-Preview
4,633
Solar-Pro-2 (31B)(high)
4,521
Solar-Open-100B
4,423
Grok-4.1-fast
4,352
A.X-4.0 (72B)
3,481
Claude-Opus-4.5
3,452
GPT-5.2 (high)
3,014
K-EXAONE-236B-A23B
2,962
Deepseek-V3.2
2,931
GPT-5.1 (high)
2,481
EXAONE-4.0.1-32B (high)
1,752