A population has a mean of µ = 30.  If 3 points are added to each score, what is the mean for the new distribution?

Group of answer choices

27

30

33

cannot be determined from the information given

When 3 points are added to each score in the population, the mean will also increase by 3 points. Here's the explanation:

- The original mean is \( \mu = 30 \).
- If you add a constant value (in this case, 3) to every score in the distribution, the mean of the new distribution will also increase by that constant.

Thus, the new mean is:
\[
\mu_{\text{new}} = 30 + 3 = 33
\]

Therefore, the correct answer is **33**.

Would you like more details on this concept or have any other questions?

Here are 5 related questions:
1. What happens to the standard deviation when a constant is added to every score in a population?
2. If each score in the population is multiplied by 2, what will happen to the mean?
3. What does it mean for a population to have a mean of 30?
4. How is the mean affected if both 3 points are added and the scores are then doubled?
5. What is the difference between population mean and sample mean?

**Tip**: Adding a constant to each score shifts the entire distribution without changing its shape or spread.

A population has a mean of µ = 30. If 3 points are added to each score, what is the mean for the new distribution?

Discover how adding 3 points to each score in a population with a mean of 30 changes the distribution. Learn key concepts in statistics and the impact of transformations on population mean, suitable for students in Grades 9-12.

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