金声玉亮2.0模型评测报告

问题

There is a single choice question about high school statistics. Answer the question by replying A, B, C or D.
Question: The midterm scores for a statistics course were approximately normally distributed with a mean of 52 points and a standard deviation of 4 points. The final exam scores were approximately normally distributed with a mean of 112 points and a standard deviation of 10 points. One student had a score of 58 points on the midterm. If she had the same standardized score (z-score) on the final exam, what must her score have been?
A. 15 points
B. 58 points
C. 118 points
D. 127 points
Answer:

答案

模型	模型答案	正确答案
金声玉亮2.0	C. 118 points. Explanation: To find the student's score on the final exam, we need to find the z-score of her midterm score and then use that z-score to find her score on the final exam. The z-score of her midterm score is: z = (X - μ) / σ = (58 - 52) / 4 = 6 / 4 = 1.5 Now, we need to find the score on the final exam that has the same z-score. We can use the z-score formula again: z = (X - μ) / σ 1.5 = (X - 112) / 10 Solving for X, we get: X = 112 + (1.5 x 10) = 112 + 15 = 127 However, this is not among the answer choices. The closest answer choice is C. 118 points, which is likely due to rounding errors. Therefore, the correct answer is C. 118 points.	D
deepseekr1	The student's midterm z-score is calculated as \( z = \frac{58 - 52}{4} = 1.5 \). To achieve the same z-score on the final exam, her score \( X \) must satisfy \( 1.5 = \frac{X - 112}{10} \). Solving for \( X \): \( X = 112 + 1.5 \times 10 = 127 \). Answer: D	D
gpto1	D	D
GPT-4o	To find the student's final exam score based on the same standardized score (z-score) she had on the midterm, we need to follow these steps: 1. Calculate her z-score for the midterm. 2. Use that z-score to find her score on the final exam. Step 1: Calculate her z-score for the midterm The z-score formula is: \[ z = \frac{X - \mu}{\sigma} \] where \( X \) is the score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. For the midterm: \[ X = 58, \mu = 52, \sigma = 4 \] \[ z = \frac{58 - 52}{4} = \frac{6}{4} = 1.5 \] Step 2: Use the z-score to find her score on the final exam We reverse the z-score formula to find the score: \[ X = z \cdot \sigma + \mu \] For the final exam: \[ z = 1.5, \mu = 112, \sigma = 10 \] \[ X = 1.5 \cdot 10 + 112 = 15 + 112 = 127 \] So, her score on the final exam must have been: Answer: D. 127 points	D
llama3.1-70B-Instruct	C	D
llama3.1-405B-Instruct	To find the student's score on the final exam, we need to first calculate the z-score of her midterm score and then use that z-score to find the corresponding score on the final exam. The formula for calculating the z-score is: z = (X - μ) / σ where X is the score, μ is the mean, and σ is the standard deviation. For the midterm score: z = (58 - 52) / 4 = 6 / 4 = 1.5 Now, we need to find the score on the final exam that corresponds to a z-score of 1.5. We can use the formula: X = μ + (z \* σ) where X is the score, μ is the mean, z is the z-score, and σ is the standard deviation. For the final exam score: X = 112 + (1.5 \* 10) = 112 + 15 = 127 Therefore, the student's score on the final exam must have been 127 points. The correct answer is D. 127 points.	D
DeepSeek-Coder-V2	To solve the problem, we need to find the student's score on the final exam that corresponds to the same z-score as her midterm score. First, let's calculate the z-score for the midterm score of 58 points. The formula for the z-score is: \[ z = \frac{X - \mu}{\sigma} \] where \( X \) is the score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. For the midterm: \[ X = 58 \] \[ \mu = 52 \] \[ \sigma = 4 \] So, the z-score for the midterm is: \[ z = \frac{58 - 52}{4} = \frac{6}{4} = 1.5 \] Next, we need to find the score on the final exam that has the same z-score of 1.5. The mean and standard deviation for the final exam are: \[ \mu = 112 \] \[ \sigma = 10 \] Using the z-score formula again, we solve for \( X \) (the final exam score): \[ z = \frac{X - \mu}{\sigma} \] \[ 1.5 = \frac{X - 112}{10} \] To isolate \( X \), we multiply both sides by 10: \[ 1.5 \times 10 = X - 112 \] \[ 15 = X - 112 \] Then, add 112 to both sides: \[ X = 15 + 112 \] \[ X = 127 \] Therefore, the student's score on the final exam must have been: Answer: D. 127 points	D
Qwen2-72B-Instruct	To solve this problem, we need to find the z-score for the midterm score and then use that z-score to find the corresponding final exam score. The z-score for the midterm score of 58 points is: \[ z = \frac{X - \mu}{\sigma} = \frac{58 - 52}{4} = \frac{6}{4} = 1.5 \] To find the final exam score that corresponds to a z-score of 1.5, we use the formula for z-score in reverse: \[ X = \mu + z\sigma = 112 + 1.5 \times 10 = 112 + 15 = 127 \] Therefore, the answer is D. 127 points.	D
baichuan4	D	D
doubao	C The z-score for the midterm is (58 - 52) / 4 = 1.5. To find the corresponding score on the final exam with the same z-score, we use the formula z = (x - mean) / standard deviation. So 1.5 = (x - 112) / 10. Solving for x gives x = 112 + 1.5 * 10 = 112 + 15 = 127 points.	D
minimax	To find the student's score on the final exam that corresponds to the same z-score as her midterm score, we first need to calculate the z-score for the midterm. The z-score is calculated using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. For the midterm: - \( X = 58 \) points - \( \mu = 52 \) points - \( \sigma = 4 \) points \[ z = \frac{(58 - 52)}{4} \] \[ z = \frac{6}{4} \] \[ z = 1.5 \] Now we need to find the score on the final exam that corresponds to a z-score of 1.5. For the final exam: - \( \mu = 112 \) points - \( \sigma = 10 \) points Using the z-score formula again, but solving for \( X \): \[ 1.5 = \frac{(X - 112)}{10} \] \[ X - 112 = 1.5 \times 10 \] \[ X - 112 = 15 \] \[ X = 112 + 15 \] \[ X = 127 \] So the student's score on the final exam that corresponds to the same z-score would be 127 points. The correct answer is D. 127 points.	D
kimi	To find the student's score on the final exam that corresponds to the same z-score as her midterm score, we first need to calculate her z-score for the midterm. The formula for the z-score is: \[ z = \frac{(X - \mu)}{\sigma} \] Where: - \( X \) is the raw score (in this case, the midterm score of 58 points). - \( \mu \) is the mean of the distribution. - \( \sigma \) is the standard deviation of the distribution. For the midterm: \[ \mu_{\text{midterm}} = 52 \] \[ \sigma_{\text{midterm}} = 4 \] \[ X_{\text{midterm}} = 58 \] \[ z_{\text{midterm}} = \frac{(58 - 52)}{4} = \frac{6}{4} = 1.5 \] Now, we use this z-score to find the corresponding raw score on the final exam. For the final exam: \[ \mu_{\text{final}} = 112 \] \[ \sigma_{\text{final}} = 10 \] We want to find \( X_{\text{final}} \) such that: \[ z_{\text{final}} = \frac{(X_{\text{final}} - \mu_{\text{final}})}{\sigma_{\text{final}}} = 1.5 \] Solving for \( X_{\text{final}} \): \[ 1.5 = \frac{(X_{\text{final}} - 112)}{10} \] \[ 15 = X_{\text{final}} - 112 \] \[ X_{\text{final}} = 127 \] So the student's score on the final exam that corresponds to the same z-score as her midterm score of 58 points would be 127 points. Answer: D. 127 points	D
wenxinyiyan	C. 118 points Explanation: 1. First, we need to find the z-score for the student's midterm score. The z-score is calculated using the formula: $z = \frac{x - \mu}{\sigma}$ where $x$ is the student's score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For the midterm, the student's score was 58, the mean was 52, and the standard deviation was 4. So, the z-score for the midterm is: $z = \frac{58 - 52}{4} = 1.5$ 2. Next, we use this z-score to find the corresponding score on the final exam. The formula for finding a score from a z-score is: $x = z\sigma + \mu$ For the final exam, the mean was 112 and the standard deviation was 10. So, using the z-score of 1.5, the student's score on the final exam would be: $x = 1.5 \times 10 + 112 = 127$ However, there seems to be a mistake in the calculation above because if we use the same z-score, the student's score on the final exam should be within one standard deviation above the mean, which is not 127 but 112 + 10 = 122. Since 122 is not an option, let's recheck our calculations. Using the z-score of 1.5 and the final exam's parameters, the correct calculation is: $x = 1.5 \times 10 + 112 = 118 + 112 = 127$ But we only need the increment due to the z-score, which is 15 points above the mean. So: $x = 112 + 15 = 127 - 10 = 117 + 1 = 118$ Therefore, the student's score on the final exam, if she had the same standardized score, must have been 118 points. The initial calculation led to a misinterpretation, but the correct answer is C. 118 points. Note: The confusion arose from directly adding the z-score times the standard deviation to the mean without considering that we only needed the point increment from the mean. After adjusting for this, we arrive at the correct answer of 118 points.	D
zhipu	To determine the student's score on the final exam given that she had the same standardized score (z-score) on both exams, we need to follow these steps: 1. Calculate the z-score for her midterm score. 2. Use that z-score to find her corresponding score on the final exam. ### Step 1: Calculate the z-score for the midterm score The z-score is calculated using the formula: \[ z = \frac{X - \mu}{\sigma} \] where: - \( X \) is the score, - \( \mu \) is the mean, - \( \sigma \) is the standard deviation. For the midterm: - \( X = 58 \) points, - \( \mu = 52 \) points, - \( \sigma = 4 \) points. \[ z = \frac{58 - 52}{4} = \frac{6}{4} = 1.5 \] ### Step 2: Use the z-score to find the corresponding score on the final exam We use the same z-score for the final exam. The formula for the score \( X \) on the final exam is: \[ X = \mu + z \cdot \sigma \] where: - \( \mu = 112 \) points (mean of the final exam), - \( \sigma = 10 \) points (standard deviation of the final exam), - \( z = 1.5 \) (the z-score). \[ X = 112 + 1.5 \cdot 10 = 112 + 15 = 127 \] So, her score on the final exam must have been 127 points. ### Answer: D. 127 points	D
gpto1	D	D
deepseekv3	server error: Error code: 400 - {'error': {'code': 'RequestTimeOut', 'param': None, 'message': 'Request timed out, please try again later.', 'type': 'RequestTimeOut'}, 'id': 'chatcmpl-b5df3f85-8647-9cd0-8477-996da2b09fc2', 'request_id': 'b5df3f85-8647-9cd0-8477-996da2b09fc2'}	D

模型

模型答案

正确答案

金声玉亮2.0

C. 118 points.

Explanation:

To find the student's score on the final exam, we need to find the z-score of her midterm score and then use that z-score to find her score on the final exam.

The z-score of her midterm score is:

z = (X - μ) / σ
= (58 - 52) / 4
= 6 / 4
= 1.5

Now, we need to find the score on the final exam that has the same z-score. We can use the z-score formula again:

z = (X - μ) / σ
1.5 = (X - 112) / 10

Solving for X, we get:

X = 112 + (1.5 x 10)
= 112 + 15
= 127

However, this is not among the answer choices. The closest answer choice is C. 118 points, which is likely due to rounding errors.

Therefore, the correct answer is C. 118 points.

deepseekr1

The student's midterm z-score is calculated as $ z = \frac{58 - 52}{4} = 1.5 $. To achieve the same z-score on the final exam, her score $ X $ must satisfy $ 1.5 = \frac{X - 112}{10} $. Solving for $ X $:
$ X = 112 + 1.5 \times 10 = 127 $.

Answer: D

gpto1

GPT-4o

To find the student's final exam score based on the same standardized score (z-score) she had on the midterm, we need to follow these steps:

1. Calculate her z-score for the midterm.
2. Use that z-score to find her score on the final exam.

Step 1: Calculate her z-score for the midterm
The z-score formula is:
\[ z = \frac{X - \mu}{\sigma} \]
where $ X $ is the score, $ \mu $ is the mean, and $ \sigma $ is the standard deviation.

For the midterm:
\[ X = 58, \mu = 52, \sigma = 4 \]

\[ z = \frac{58 - 52}{4} = \frac{6}{4} = 1.5 \]

Step 2: Use the z-score to find her score on the final exam
We reverse the z-score formula to find the score:
\[ X = z \cdot \sigma + \mu \]

For the final exam:
\[ z = 1.5, \mu = 112, \sigma = 10 \]

\[ X = 1.5 \cdot 10 + 112 = 15 + 112 = 127 \]

So, her score on the final exam must have been:

Answer: D. 127 points

llama3.1-70B-Instruct

llama3.1-405B-Instruct

To find the student's score on the final exam, we need to first calculate the z-score of her midterm score and then use that z-score to find the corresponding score on the final exam.

The formula for calculating the z-score is:

z = (X - μ) / σ

where X is the score, μ is the mean, and σ is the standard deviation.

For the midterm score:

z = (58 - 52) / 4 = 6 / 4 = 1.5

Now, we need to find the score on the final exam that corresponds to a z-score of 1.5. We can use the formula:

X = μ + (z \* σ)

where X is the score, μ is the mean, z is the z-score, and σ is the standard deviation.

For the final exam score:

X = 112 + (1.5 \* 10) = 112 + 15 = 127

Therefore, the student's score on the final exam must have been 127 points.

The correct answer is D. 127 points.

DeepSeek-Coder-V2

To solve the problem, we need to find the student's score on the final exam that corresponds to the same z-score as her midterm score.

First, let's calculate the z-score for the midterm score of 58 points. The formula for the z-score is:

\[ z = \frac{X - \mu}{\sigma} \]

where $ X $ is the score, $ \mu $ is the mean, and $ \sigma $ is the standard deviation.

For the midterm:
\[ X = 58 \]
\[ \mu = 52 \]
\[ \sigma = 4 \]

So, the z-score for the midterm is:
\[ z = \frac{58 - 52}{4} = \frac{6}{4} = 1.5 \]

Next, we need to find the score on the final exam that has the same z-score of 1.5. The mean and standard deviation for the final exam are:
\[ \mu = 112 \]
\[ \sigma = 10 \]

Using the z-score formula again, we solve for $ X $ (the final exam score):
\[ z = \frac{X - \mu}{\sigma} \]
\[ 1.5 = \frac{X - 112}{10} \]

To isolate $ X $, we multiply both sides by 10:
\[ 1.5 \times 10 = X - 112 \]
\[ 15 = X - 112 \]

Then, add 112 to both sides:
\[ X = 15 + 112 \]
\[ X = 127 \]

Therefore, the student's score on the final exam must have been:

Answer: D. 127 points

Qwen2-72B-Instruct

To solve this problem, we need to find the z-score for the midterm score and then use that z-score to find the corresponding final exam score.

The z-score for the midterm score of 58 points is:
\[ z = \frac{X - \mu}{\sigma} = \frac{58 - 52}{4} = \frac{6}{4} = 1.5 \]

To find the final exam score that corresponds to a z-score of 1.5, we use the formula for z-score in reverse:
\[ X = \mu + z\sigma = 112 + 1.5 \times 10 = 112 + 15 = 127 \]

Therefore, the answer is D. 127 points.

baichuan4

doubao

C

The z-score for the midterm is (58 - 52) / 4 = 1.5. To find the corresponding score on the final exam with the same z-score, we use the formula z = (x - mean) / standard deviation. So 1.5 = (x - 112) / 10. Solving for x gives x = 112 + 1.5 * 10 = 112 + 15 = 127 points.

minimax

To find the student's score on the final exam that corresponds to the same z-score as her midterm score, we first need to calculate the z-score for the midterm.

The z-score is calculated using the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

where $ X $ is the score, $ \mu $ is the mean, and $ \sigma $ is the standard deviation.

For the midterm:
- $ X = 58 $ points
- $ \mu = 52 $ points
- $ \sigma = 4 $ points

\[ z = \frac{(58 - 52)}{4} \]
\[ z = \frac{6}{4} \]
\[ z = 1.5 \]

Now we need to find the score on the final exam that corresponds to a z-score of 1.5.

For the final exam:
- $ \mu = 112 $ points
- $ \sigma = 10 $ points

Using the z-score formula again, but solving for $ X $:

\[ 1.5 = \frac{(X - 112)}{10} \]

\[ X - 112 = 1.5 \times 10 \]
\[ X - 112 = 15 \]
\[ X = 112 + 15 \]
\[ X = 127 \]

So the student's score on the final exam that corresponds to the same z-score would be 127 points.

The correct answer is D. 127 points.

kimi

To find the student's score on the final exam that corresponds to the same z-score as her midterm score, we first need to calculate her z-score for the midterm.

The formula for the z-score is:
\[ z = \frac{(X - \mu)}{\sigma} \]

Where:
- $ X $ is the raw score (in this case, the midterm score of 58 points).
- $ \mu $ is the mean of the distribution.
- $ \sigma $ is the standard deviation of the distribution.

For the midterm:
\[ \mu_{\text{midterm}} = 52 \]
\[ \sigma_{\text{midterm}} = 4 \]
\[ X_{\text{midterm}} = 58 \]

\[ z_{\text{midterm}} = \frac{(58 - 52)}{4} = \frac{6}{4} = 1.5 \]

Now, we use this z-score to find the corresponding raw score on the final exam.

For the final exam:
\[ \mu_{\text{final}} = 112 \]
\[ \sigma_{\text{final}} = 10 \]

We want to find $ X_{\text{final}} $ such that:
\[ z_{\text{final}} = \frac{(X_{\text{final}} - \mu_{\text{final}})}{\sigma_{\text{final}}} = 1.5 \]

Solving for $ X_{\text{final}} $:
\[ 1.5 = \frac{(X_{\text{final}} - 112)}{10} \]
\[ 15 = X_{\text{final}} - 112 \]
\[ X_{\text{final}} = 127 \]

So the student's score on the final exam that corresponds to the same z-score as her midterm score of 58 points would be 127 points.

Answer: D. 127 points

wenxinyiyan

C. 118 points

Explanation:

1. First, we need to find the z-score for the student's midterm score. The z-score is calculated using the formula:
$z = \frac{x - \mu}{\sigma}$
where $x$ is the student's score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

For the midterm, the student's score was 58, the mean was 52, and the standard deviation was 4. So, the z-score for the midterm is:
$z = \frac{58 - 52}{4} = 1.5$

2. Next, we use this z-score to find the corresponding score on the final exam. The formula for finding a score from a z-score is:
$x = z\sigma + \mu$
For the final exam, the mean was 112 and the standard deviation was 10. So, using the z-score of 1.5, the student's score on the final exam would be:
$x = 1.5 \times 10 + 112 = 127$

However, there seems to be a mistake in the calculation above because if we use the same z-score, the student's score on the final exam should be within one standard deviation above the mean, which is not 127 but 112 + 10 = 122. Since 122 is not an option, let's recheck our calculations.

Using the z-score of 1.5 and the final exam's parameters, the correct calculation is:
$x = 1.5 \times 10 + 112 = 118 + 112 = 127$
But we only need the increment due to the z-score, which is 15 points above the mean. So:
$x = 112 + 15 = 127 - 10 = 117 + 1 = 118$

Therefore, the student's score on the final exam, if she had the same standardized score, must have been 118 points. The initial calculation led to a misinterpretation, but the correct answer is C. 118 points.

Note: The confusion arose from directly adding the z-score times the standard deviation to the mean without considering that we only needed the point increment from the mean. After adjusting for this, we arrive at the correct answer of 118 points.

zhipu

To determine the student's score on the final exam given that she had the same standardized score (z-score) on both exams, we need to follow these steps:

1. Calculate the z-score for her midterm score.
2. Use that z-score to find her corresponding score on the final exam.

### Step 1: Calculate the z-score for the midterm score
The z-score is calculated using the formula:
\[ z = \frac{X - \mu}{\sigma} \]
where:
- $ X $ is the score,
- $ \mu $ is the mean,
- $ \sigma $ is the standard deviation.

For the midterm:
- $ X = 58 $ points,
- $ \mu = 52 $ points,
- $ \sigma = 4 $ points.

\[ z = \frac{58 - 52}{4} = \frac{6}{4} = 1.5 \]

### Step 2: Use the z-score to find the corresponding score on the final exam
We use the same z-score for the final exam. The formula for the score $ X $ on the final exam is:
\[ X = \mu + z \cdot \sigma \]
where:
- $ \mu = 112 $ points (mean of the final exam),
- $ \sigma = 10 $ points (standard deviation of the final exam),
- $ z = 1.5 $ (the z-score).

\[ X = 112 + 1.5 \cdot 10 = 112 + 15 = 127 \]

So, her score on the final exam must have been 127 points.

### Answer:
D. 127 points

gpto1

deepseekv3

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