Students were given an exam with 300 multiple-choice questions. The distribution of the scores was normal and mean was 195 with a standard deviation of 30.

What was the score of students who scored in the middle of the class? (50% did better, 50% did worse).

wouldn't it be the mean?

The mean is 195. Is that the middle score of the class? I'm very confused. The text that I have is not showing how to solve this problem. AHHH

The distribution is normal, thus symmetric about the mean, so the mean is also the median. You are looking for the median.

So is the answer 195?

Thanks for the help! Awesome!

To find the score of students who scored in the middle of the class (where 50% did better and 50% did worse), we need to find the corresponding z-score and then use it to calculate the actual score.

1. Convert the given mean and standard deviation to z-scores using the formula: z = (x - μ) / σ, where x is the individual score, μ is the mean, and σ is the standard deviation.

2. Since we want to find the score of students who scored in the middle of the class (50% did better and 50% did worse), we need to find the z-score that represents the cumulative normal distribution of 0.50.

3. Use a standard Normal Distribution table or a statistical software to look up the z-score corresponding to a cumulative probability of 0.50.

4. Once you have obtained the z-score, use the formula to convert it back to the actual score: x = (z * σ) + μ.

Applying these steps to the given information:

1. Let's use the formula to find the z-score:
z = (x - μ) / σ, where x is the individual score, μ is the mean (195), and σ is the standard deviation (30).

2. We want to find the cumulative probability of 0.50, which corresponds to the middle of the distribution.

3. Use the standard Normal Distribution table or a statistical software to find the z-score with a cumulative probability of 0.50. In this case, the z-score is 0.

4. Finally, use the formula to convert the z-score back to the actual score:
x = (z * σ) + μ
= (0 * 30) + 195
= 195.

Therefore, the score of the students who scored in the middle of the class is 195.