​(c) According to the empirical​ rule, 95% of days in the month will be between what two​ temperatures?

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The empirical rule (also known as the 68-95-99.7 rule) states that for a normally distributed dataset:

- Approximately 68% of the data falls within one standard deviation (\(\sigma\)) of the mean (\(\mu\)).
- Approximately 95% of the data falls within two standard deviations (\(\sigma\)) of the mean (\(\mu\)).
- Approximately 99.7% of the data falls within three standard deviations (\(\sigma\)) of the mean (\(\mu\)).

Since you are asked to find the range that contains 95% of the days, you'll use the second part of the empirical rule, which is within two standard deviations from the mean.

### Calculation:
\[
\text{Lower limit} = \mu - 2\sigma
\]
\[
\text{Upper limit} = \mu + 2\sigma
\]

Given:
- Mean (\(\mu\)) = 80.8
- Standard deviation (\(\sigma\)) = 8.2

Let's calculate the limits.According to the empirical rule, 95% of the days in the month will have temperatures between approximately **64.4°F** and **97.2°F**.

Would you like more details, or do you have any questions?

Here are some related questions:
1. How does the empirical rule apply to non-normally distributed data?
2. What would be the temperature range for 68% of the days using the empirical rule?
3. How might extreme temperatures affect the interpretation of the empirical rule?
4. What steps could be taken to verify if the temperature data is normally distributed?
5. How does the range for 95% compare to the full range of temperatures recorded?

**Tip:** The empirical rule is a quick way to estimate the spread of data, but it's most accurate when the data is normally distributed. Always consider the shape of the distribution when using it.

Explore how the empirical rule applies to temperature data with a focus on calculating the range for 95% of days in a month. Learn about normal distribution, standard deviations, and statistical estimation. Includes a detailed calculation example with mean = 80.8°F and standard deviation = 8.2°F.

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