# Lesson 10Meaningful PossibilitiesSolidify Understanding

## Learning Focus

Use simulation to find a plausible interval for the mean of a population from a sample.

How does finding an interval for a population mean compare to finding an interval for a population proportion?

## Open Up the Math: Launch, Explore, Discuss

Alyce, Javier, and Veronica are thinking about the original artifacts they had collected earlier and they are wondering if they can develop a strategy for finding an interval of reasonable values for the average age of the artifacts by taking a sample of artifacts.

### 1.

Design and carry out a simulation you could use to create an interval of reasonable values for the actual average age of the artifacts.

### 2.

Alyce randomly selects artifacts and finds that years and years. Using the work from your simulation, design and use a strategy that does not require simulations to find an interval of plausible values for the average age of the artifacts in the bag.

### 3.

If the average age of the artifacts was really years old with , how likely would you be to take a sample of artifacts and get an average age of or higher?

### 4.

Explain why a sample size of is useful for this problem.

### 5.

Compare your strategy to the one you developed in the last lesson. Give a general strategy for finding an interval of plausible values for a population parameter using either a sample mean or a sample proportion.

What could be done to reduce the size of the interval in problem 2 and still have a high degree of confidence that it represents the population mean?

## Takeaways

For sample mean, = sample standard deviation

Margin of error for a sample mean:

Interval of plausible values from a sample mean:

## Lesson Summary

In this lesson, we found a margin of error for a sample mean, which creates a plausible interval for the population mean. We learned that to use the margin of error formula, we must have a sample size of at least 30. We also learned how to find the likelihood that a sample comes from a population with a given mean and standard deviation.

## Retrieval

Given:

### 1.

Write the dimensions of and . Explain how you know whether or not you can multiply these two matrices.

Find .

Factor .

Factor .

Factor .