Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A.

Select all that apply:

A has the larger mean.

B has the larger mean.

The means of A and B are equal.

A has the larger standard deviation.

B has the larger standard deviation.

The standard deviations of A and B are equal.

From the description of the two normal distributions:

1. **A and B are centered at the same point**, meaning that their means are equal. So, the correct statement is:
   - **The means of A and B are equal.**

2. **B is narrower and taller**, while **A is wider**. This suggests that **B has a smaller standard deviation** (because narrower distributions have smaller standard deviations), and **A has a larger standard deviation** (because wider distributions have larger standard deviations). So, the correct statement is:
   - **A has the larger standard deviation**.

Therefore, the correct answers are:

- **The means of A and B are equal.**
- **A has the larger standard deviation.**

### Would you like more details or have any questions?

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Here are 5 related questions that expand on the concept:

1. How does the standard deviation affect the shape of a normal distribution?
2. What is the relationship between the mean and the median in a symmetric normal distribution?
3. How would you calculate the mean and standard deviation from a given dataset?
4. What is the probability of a data point lying within one standard deviation of the mean in a normal distribution?
5. How do z-scores relate to the standard deviation in a normal distribution?

**Tip**: A narrower distribution indicates that data points are more concentrated around the mean, meaning a smaller standard deviation.

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A.

Select all that apply:

A has the larger mean.
B has the larger mean.
The means of A and B are equal.
A has the larger standard deviation.
B has the larger standard deviation.
The standard deviations of A and B are equal.

Analyze the properties of normal distributions through a comparison of two curves, A and B. Learn how the mean and standard deviation affect the shape and spread of distributions. Suitable for students in Grades 10-12, this problem demonstrates key concepts such as mean equality and standard deviation differences.

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