| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D. The woman, because her height is 1.33 standard deviations above the mean height of all women, whereas the man’s height is only one standard deviation above the mean height of all men. |
D |
| deepseekr1 | The answer is D. To determine who is more unusually tall, we compare their z-scores, which standardize deviations from the mean. - **Man's z-score**: (74 - 70) / 4 = 1.0. - **Woman's z-score**: (70 - 66) / 3 ≈ 1.33. The woman's z-score is higher, meaning her height is farther above her group's mean in standard deviation terms. This makes her more unusually tall relative to her sex than the man is relative to his. **Answer: D** |
D |
| gpto1 | D | D |
| GPT-4o | D. The woman, because her height is 1.33 standard deviations above the mean height of all women, whereas the man’s height is only one standard deviation above the mean height of all men. | D |
| llama3.1-70B-Instruct | D |
D |
| llama3.1-405B-Instruct | D. The woman is more unusually tall within her respective sex. The man is only one standard deviation above the mean height of all men, whereas the woman is 1.33 standard deviations above the mean height of all women. Choice (A) is incorrect because the mean heights for the two groups are different. Choice (B) is incorrect because the standard deviations of the heights for the two groups are different. Choice (C) is incorrect because the man is 74 inches tall and the woman is only 70 inches tall. The best answer is D. |
D |
| DeepSeek-Coder-V2 | D | D |
| Qwen2-72B-Instruct | D. The woman, because her height is 1.33 standard deviations above the mean height of all women, whereas the man’s height is only one standard deviation above the mean height of all men. | D |
| baichuan4 | D | D |
| doubao | D For the man, 74 inches is 74 - 70 = 4 inches above the mean of 70 inches, which is 4 / 4 = 1 standard deviation above the mean. For the woman, 70 inches is 70 - 66 = 4 inches above the mean of 66 inches, and 4 / 3 ≈ 1.33 standard deviations above the mean. Since 1.33 > 1, the woman is more unusually tall within her sex. |
D |
| minimax | D. The woman, because her height is 1.33 standard deviations above the mean height of all women, whereas the man’s height is only one standard deviation above the mean height of all men. | D |
| kimi | D. The woman, because her height is 1.33 standard deviations above the mean height of all women, whereas the man’s height is only one standard deviation above the mean height of all men. To calculate how many standard deviations above the mean each person's height is, you use the formula: \[ Z = \frac{(X - \mu)}{\sigma} \] where \( Z \) is the number of standard deviations from the mean, \( X \) is the individual's height, \( \mu \) is the mean height, and \( \sigma \) is the standard deviation. For the man: \[ Z_{man} = \frac{(74 - 70)}{4} = \frac{4}{4} = 1 \] For the woman: \[ Z_{woman} = \frac{(70 - 66)}{3} = \frac{4}{3} \approx 1.33 \] So the woman is more unusually tall within her respective sex. |
D |
| wenxinyiyan | D | D |
| zhipu | D. The woman, because her height is 1.33 standard deviations above the mean height of all women, whereas the man’s height is only one standard deviation above the mean height of all men. Explanation: To determine who is more unusually tall within their respective sex, we can calculate how many standard deviations each person's height is above the mean for their respective group. For the man: - Mean height of adult men = 70 inches - Standard deviation = 4 inches - Height of the man = 74 inches - Number of standard deviations above the mean = (74 - 70) / 4 = 1 For the woman: - Mean height of adult women = 66 inches - Standard deviation = 3 inches - Height of the woman = 70 inches - Number of standard deviations above the mean = (70 - 66) / 3 ≈ 1.33 Since the woman's height is 1.33 standard deviations above the mean height of all women, which is higher than the man's height of 1 standard deviation above the mean height of all men, the woman is more unusually tall within her sex. Therefore, the correct answer is D. |
D |
| gpto1 | D | D |
| deepseekv3 | To determine who is more unusually tall within their respective sex, we need to calculate the z-scores for both individuals. The z-score measures how many standard deviations an individual's height is from the mean height of their sex. ### For the man: - Mean height of men = 70 inches - Standard deviation of men's height = 4 inches - Height of the man = 74 inches \[ \text{Z-score for the man} = \frac{74 - 70}{4} = 1 \] The man's height is 1 standard deviation above the mean height of men. ### For the woman: - Mean height of women = 66 inches - Standard deviation of women's height = 3 inches - Height of the woman = 70 inches \[ \text{Z-score for the woman} = \frac{70 - 66}{3} = 1.33 \] The woman's height is 1.33 standard deviations above the mean height of women. ### Conclusion: The woman has a higher z-score (1.33) compared to the man's z-score (1), which means she is more unusually tall within her respective sex. Thus, the correct answer is: **D. The woman, because her height is 1.33 standard deviations above the mean height of all women, whereas the man’s height is only one standard deviation above the mean height of all men.** |
D |