问题


There is a single choice question about high school statistics. Answer the question by replying A, B, C or D.
Question: The observed times (in minutes) it takes a runner to complete a marathon are normally distributed. The z-score for his running time this week is –2. Which one of the following statements is a correct interpretation of his z-score?
A. This week his time was two minutes lower than his time last week.
B. This week his time was two minutes lower than his best time ever.
C. This week his time was two minutes lower than his average time.
D. This week his time was two standard deviations lower than his average time.
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

D. This week his time was two standard deviations lower than his average time.		 D
deepseekr1

The z-score of -2 indicates the runner's time this week is 2 standard deviations below his average time. This interpretation directly aligns with the definition of a z-score, which measures how many standard deviations a value is from the mean. Options A, B, and C incorrectly reference minutes rather than standard deviations or compare to unrelated times (last week, best time).

Answer: D		 D
gpto1 D D
GPT-4o D. This week his time was two standard deviations lower than his average time. D
llama3.1-70B-Instruct

D		 D
llama3.1-405B-Instruct

D. The z -score is a measure of how many standard deviations an observation is away from the mean. A negative z -score means the observation is below the mean. Therefore, a z -score of –2 means the runner’s time was two standard deviations below his average time.
The best answer is D.		 D
DeepSeek-Coder-V2 D D
Qwen2-72B-Instruct D. This week his time was two standard deviations lower than his average time. D
baichuan4 D D
doubao D D
minimax D. This week his time was two standard deviations lower than his average time. D
kimi D. This week his time was two standard deviations lower than his average time. D
wenxinyiyan D D
zhipu D

A z-score of –2 indicates that the runner's time this week was 2 standard deviations below the mean (average) time. This is a correct interpretation of the z-score in the context of a normal distribution. The other options do not accurately describe the meaning of a z-score.		 D
gpto1 D D
deepseekv3 D. This week his time was two standard deviations lower than his average time.

Explanation: A z-score represents the number of standard deviations a data point is from the mean of the distribution. A z-score of –2 means the runner's time this week was 2 standard deviations below his average time. It does not directly compare to last week's time, his best time, or a fixed number of minutes (e.g., two minutes).		 D