Problem Analysis #25

Kimi K3 · Run 1

Correct

16.61s

702 toks

API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.

Problem Statement

This is a Korean CSAT mathematics multiple-choice problem. Solve it and put only the correct choice symbol, one of ①, ②, ③, ④, ⑤, inside \boxed{}.

Problem 26 A population is normally distributed with meanmand standard deviation 5. From this population, a random sample of size 36 is taken, and a 99% confidence interval for the population meanmis constructed using the sample mean. The resulting confidence in- terval is 1.2≤m≤a. Find the value ofa. (Here,Zdenotes a standard normal random variable, and use P(|Z| ≤2.58) = 0.99.) [3 points] ①5.1 ②5.2 ③5.3 ④5.4 ⑤5.5

Ground Truth

⑤

Recorded model response / solution

Reasoning Process

The standard error is $\frac{5}{\sqrt{36}}=\frac{5}{6}$ .

For a 99% confidence interval, the margin of error is

2.58\cdot \frac{5}{6}=2.15.

So the interval width is $2(2.15)=4.3$ . Given the lower bound $1.2$ ,

a-1.2=4.3 \implies a=5.5.

\boxed{⑤}

Final Model Output

⑤

Comparative Analysis (P25) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

Motif 3

15.3

Kimi K3

12.1

Solar Pro 4

8.9

K-EXAONE-2

1.0

Avg Token Usage

Solar Pro 4

823.7

Kimi K3

756.7

K-EXAONE-2

504.7